Projective representations of $S_n$: ring structure and inductive formulae

P. Hoffman

Displaying similar documents to “Projective representations of $S_{n}$ : ring structure and inductive formulae”

The ideal of relations for the ring of invariants of $n$ points on the line

Benjamin Howard, John J. Millson, Andrew Snowden, Ravi Vakil (2012)

Journal of the European Mathematical Society

Similarity:

The ring of projective invariants of $n$ ordered points on the projective line is one of the most basic and earliest studied examples in Geometric Invariant Theory. It is a remarkable fact and the point of this paper that, unlike its close relative the ring of invariants of $n$ unordered points, this ring can be completely and simply described. In 1894 Kempe found generators for this ring, thereby proving the First Main Theorem for it (in the terminology introduced by Weyl). In this paper...

Brauer relations in finite groups

Alex Bartel, Tim Dokchitser (2015)

Journal of the European Mathematical Society

Similarity:

If $G$ is a non-cyclic finite group, non-isomorphic $G$ -sets $X, Y$ may give rise to isomorphic permutation representations $ℂ [X] ≅ ℂ [Y]$ . Equivalently, the map from the Burnside ring to the rational representation ring of $G$ has a kernel. Its elements are called Brauer relations, and the purpose of this paper is to classify them in all finite groups, extending the Tornehave–Bouc classification in the case of $p$ -groups.

Skew inverse power series rings over a ring with projective socle

Kamal Paykan (2017)

Czechoslovak Mathematical Journal

Similarity:

A ring $R$ is called a right $PS$ -ring if its socle, $Soc (R_{R})$ , is projective. Nicholson and Watters have shown that if $R$ is a right $PS$ -ring, then so are the polynomial ring $R [x]$ and power series ring $R [[x]]$ . In this paper, it is proved that, under suitable conditions, if $R$ has a (flat) projective socle, then so does the skew inverse power series ring $R [[x^{- 1}; α, δ]]$ and the skew polynomial ring $R [x; α, δ]$ , where $R$ is an associative ring equipped with an automorphism $α$ and an $α$ -derivation $δ$ . Our results extend and unify many existing...

On indecomposable projective representations of finite groups over fields of characteristic p > 0

Leonid F. Barannyk, Kamila Sobolewska (2003)

Colloquium Mathematicae

Similarity:

Let G be a finite group, F a field of characteristic p with p||G|, and $F^{λ} G$ the twisted group algebra of the group G and the field F with a 2-cocycle λ ∈ Z²(G,F*). We give necessary and sufficient conditions for $F^{λ} G$ to be of finite representation type. We also introduce the concept of projective F-representation type for the group G (finite, infinite, mixed) and we exhibit finite groups of each type.

The projective limit of the $H^{p}$ spaces

J. A. Cima, J. R. Harrington, J. A. Pfaltzgraff (1977)

Colloquium Mathematicae

Similarity:

Special Grassmann manifolds $V_{3}^{4}$ in the projective space $P_{7}$

Josef Vala (1988)

Časopis pro pěstování matematiky

Similarity:

Twisted group rings of strongly unbounded representation type

Leonid F. Barannyk, Dariusz Klein (2004)

Colloquium Mathematicae

Similarity:

Let S be a commutative local ring of characteristic p, which is not a field, S* the multiplicative group of S, W a subgroup of S*, G a finite p-group, and $S^{λ} G$ a twisted group ring of the group G and of the ring S with a 2-cocycle λ ∈ Z²(G,S*). Denote by $I n d_{m} (S^{λ} G)$ the set of isomorphism classes of indecomposable $S^{λ} G$ -modules of S-rank m. We exhibit rings $S^{λ} G$ for which there exists a function $f_{λ} : ℕ \to ℕ$ such that $f_{λ} (n) \geq n$ and $I n d_{f_{λ} (n)} (S^{λ} G)$ is an infinite set for every natural n > 1. In special cases $f_{λ} (ℕ)$ contains every natural...

Finite groups of OTP projective representation type over a complete discrete valuation domain of positive characteristic

Leonid F. Barannyk, Dariusz Klein (2012)

Colloquium Mathematicae

Similarity:

Let S be a commutative complete discrete valuation domain of positive characteristic p, S* the unit group of S, Ω a subgroup of S* and $G = G_{p} \times B$ a finite group, where $G_{p}$ is a p-group and B is a p’-group. Denote by $S^{λ} G$ the twisted group algebra of G over S with a 2-cocycle λ ∈ Z²(G,S*). For Ω satisfying a specific condition, we give necessary and sufficient conditions for G to be of OTP projective (S,Ω)-representation type, in the sense that there exists a cocycle λ ∈ Z²(G,Ω) such that every indecomposable...

Projective invariant metrics and open convex regular cones. I

Fabio Podestà (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Similarity:

In this work we give a characterization of the projective invariant pseudometric $P$ , introduced by H. Wu, for a particular class of real $\mathbf{C}^{\infty}$ -manifolds; in view of this result, we study the group of projective transformations for the same class of manifolds and we determine the integrated pseudodistance $p$ of $P$ in open convex regular cones of $\mathbb{R}^{n}$ , endowed with the characteristic metric.

Projective invariant metrics and open convex regular cones. I

Fabio Podestà (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

Stacks of group representations

Paul Balmer (2015)

Journal of the European Mathematical Society

Similarity:

We start with a small paradigm shift about group representations, namely the observation that restriction to a subgroup can be understood as an extension-of-scalars. We deduce that, given a group $G$ , the derived and the stable categories of representations of a subgroup $H$ can be constructed out of the corresponding category for $G$ by a purely triangulated-categorical construction, analogous to étale extension in algebraic geometry. In the case of finite groups, we then use descent methods...

Finite groups of OTP projective representation type

Leonid F. Barannyk (2012)

Colloquium Mathematicae

Similarity:

Let K be a field of characteristic p > 0, K* the multiplicative group of K and $G = G_{p} \times B$ a finite group, where $G_{p}$ is a p-group and B is a p’-group. Denote by $K^{λ} G$ a twisted group algebra of G over K with a 2-cocycle λ ∈ Z²(G,K*). We give necessary and sufficient conditions for G to be of OTP projective K-representation type, in the sense that there exists a cocycle λ ∈ Z²(G,K*) such that every indecomposable $K^{λ} G$ -module is isomorphic to the outer tensor product V W of an indecomposable $K^{λ} G_{p}$ -module...

Projective abelian Hopf algebras over a field

Andrzej Skowroński

Similarity:

CONTENTSIntroduction............................................................................................................................................51. Cohen schemes.................................................................................................................................72. Projective abelian Hopf algebras......................................................................................................113. The structure of groups $H o m_{ℋ ₁} (^{m} P,^{n} P)$ ..............................................................................174....

On faithful projective representations of finite abelian p-groups over a field of characteristic p

Leonid F. Barannyk (2008)

Colloquium Mathematicae

Similarity:

Let G be a noncyclic abelian p-group and K be an infinite field of finite characteristic p. For every 2-cocycle λ ∈ Z²(G,K*) such that the twisted group algebra $K^{λ} G$ is of infinite representation type, we find natural numbers d for which G has infinitely many faithful absolutely indecomposable λ-representations over K of dimension d.

Generic representations of orthogonal groups: projective functors in the category $ℱ_{q u a d}$

Christine Vespa (2008)

Fundamenta Mathematicae

Similarity:

We continue the study of the category of functors $ℱ_{q u a d}$ , associated to ₂-vector spaces equipped with a nondegenerate quadratic form, initiated in J. Pure Appl. Algebra 212 (2008) and Algebr. Geom. Topology 7 (2007). We define a filtration of the standard projective objects in $ℱ_{q u a d}$ ; this refines to give a decomposition into indecomposable factors of the first two standard projective objects in $ℱ_{q u a d}$ : $P_{H ₀}$ and $P_{H ₁}$ . As an application of these two decompositions, we give a complete description of the polynomial...

About G-rings

Najib Mahdou (2017)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

In this paper, we are concerned with G-rings. We generalize the Kaplansky’s theorem to rings with zero-divisors. Also, we assert that if $R \subseteq T$ is a ring extension such that $m T \subseteq R$ for some regular element $m$ of $T$ , then $T$ is a G-ring if and only if so is $R$ . Also, we examine the transfer of the G-ring property to trivial ring extensions. Finally, we conclude the paper with illustrative examples discussing the utility and limits of our results.

A Note on Lax Projective Embeddings of Grassmann Spaces

Eva Ferrara Dentice (2018)

Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche

Similarity:

In the paper (Ferrara Dentice et al., 2004) a complete exposition of the state of the art for lax embeddings of polar spaces of ﬁnite rank $\geq 3$ is presented. As a consequence, we have that if a Grassmann space $G$ of dimension 3 and index 1 has a lax embedding in a projective space over a skew–ﬁeld $K$ , then $G$ is the Klein quadric deﬁned over a subﬁeld of $K$ . In this paper, I examine Grassmann spaces of arbitrary dimension $d\geq 3$ and index $h\geq 1$ having a lax embedding in a projective space.

Finite-dimensional twisted group algebras of semi-wild representation type

Leonid F. Barannyk (2010)

Colloquium Mathematicae

Similarity:

Let G be a finite group, K a field of characteristic p > 0, and $K^{λ} G$ the twisted group algebra of G over K with a 2-cocycle λ ∈ Z²(G,K*). We give necessary and sufficient conditions for $K^{λ} G$ to be of semi-wild representation type in the sense of Drozd. We also introduce the concept of projective K-representation type for a finite group (tame, semi-wild, purely semi-wild) and we exhibit finite groups of each type.

On symmetric functions and the spin characters of $S_{n}$

John R. Stembridge (1990)

Banach Center Publications

Similarity:

Representations of modules over a *-algebra and related seminorms

Camillo Trapani, Salvatore Triolo (2008)

Studia Mathematica

Similarity:

Representations of a module over a *-algebra $_{}$ are considered and some related seminorms are constructed and studied, with the aim of finding bounded *-representations of $_{}$ .

Diagonals of projective tensor products and orthogonally additive polynomials

Qingying Bu, Gerard Buskes (2014)

Studia Mathematica

Similarity:

Let E be a Banach space with 1-unconditional basis. Denote by $Δ (\otimes ̂_{n, π} E)$ (resp. $Δ (\otimes ̂_{n, s, π} E)$ ) the main diagonal space of the n-fold full (resp. symmetric) projective Banach space tensor product, and denote by $Δ (\otimes ̂_{n, | π |} E)$ (resp. $Δ (\otimes ̂_{n, s, | π |} E)$ ) the main diagonal space of the n-fold full (resp. symmetric) projective Banach lattice tensor product. We show that these four main diagonal spaces are pairwise isometrically isomorphic, and in addition, that they are isometrically lattice isomorphic to $E_{[n]}$ , the completion of the n-concavification...

On some noetherian rings of $C^{\infty}$ germs on a real closed field

Abdelhafed Elkhadiri (2011)

Annales Polonici Mathematici

Similarity:

Let R be a real closed field, and denote by $_{R, n}$ the ring of germs, at the origin of Rⁿ, of $C^{\infty}$ functions in a neighborhood of 0 ∈ Rⁿ. For each n ∈ ℕ, we construct a quasianalytic subring $_{R, n} \subset_{R, n}$ with some natural properties. We prove that, for each n ∈ ℕ, $_{R, n}$ is a noetherian ring and if R = ℝ (the field of real numbers), then $_{ℝ, n} = ₙ$ , where ₙ is the ring of germs, at the origin of ℝⁿ, of real analytic functions. Finally, we prove the Real Nullstellensatz and solve Hilbert’s 17th Problem for the ring $_{R, n}$ . ...

On stable equivalences of module subcategories over a semiperfect noetherian ring

Noritsugu Kameyama, Yuko Kimura, Kenji Nishida (2014)

Colloquium Mathematicae

Similarity:

Given a semiperfect two-sided noetherian ring Λ, we study two subcategories $_{k} (Λ) = M \in m o d Λ | E x t_{Λ}^{j} (T r M, Λ) = 0 (1 \leq j \leq k)$ and $_{k} (Λ) = N \in m o d Λ | E x t_{Λ}^{j} (N, Λ) = 0 (1 \leq j \leq k)$ of the category mod Λ of finitely generated right Λ-modules, where Tr M is Auslander’s transpose of M. In particular, we give another convenient description of the categories $_{k} (Λ)$ and $_{k} (Λ)$ , and we study category equivalences and stable equivalences between them. Several results proved in [J. Algebra 301 (2006), 748-780] are extended to the case when Λ is a two-sided noetherian semiperfect ring.

Semigroup actions on tori and stationary measures on projective spaces

Yves Guivarc&#039;h, Roman Urban (2005)

Studia Mathematica

Similarity:

Let Γ be a subsemigroup of G = GL(d,ℝ), d > 1. We assume that the action of Γ on $ℝ^{d}$ is strongly irreducible and that Γ contains a proximal and quasi-expanding element. We describe contraction properties of the dynamics of Γ on $ℝ^{d}$ at infinity. This amounts to the consideration of the action of Γ on some compact homogeneous spaces of G, which are extensions of the projective space $ℙ^{d - 1}$ . In the case where Γ is a subsemigroup of GL(d,ℝ) ∩ M(d,ℤ) and Γ has the above properties, we deduce that...

Representations of $S_{n}$ and $G L_{n}$ and the q-Schur algebra

Gordon James (1990)

Banach Center Publications

Similarity:

Displaying similar documents to “Projective representations of S n : ring structure and inductive formulae”

Displaying similar documents to “Projective representations of $S_{n}$ : ring structure and inductive formulae”