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

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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

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If G is a non-cyclic finite group, non-isomorphic G -sets X , Y may give rise to isomorphic permutation representations [ X ] [ 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

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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

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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.

Gorenstein projective complexes with respect to cotorsion pairs

Renyu Zhao, Pengju Ma (2019)

Czechoslovak Mathematical Journal

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Let ( 𝒜 , ) be a complete and hereditary cotorsion pair in the category of left R -modules. In this paper, the so-called Gorenstein projective complexes with respect to the cotorsion pair ( 𝒜 , ) are introduced. We show that these complexes are just the complexes of Gorenstein projective modules with respect to the cotorsion pair ( 𝒜 , ) . As an application, we prove that both the Gorenstein projective modules with respect to cotorsion pairs and the Gorenstein projective complexes with respect to cotorsion...

Twisted group rings of strongly unbounded representation type

Leonid F. Barannyk, Dariusz Klein (2004)

Colloquium Mathematicae

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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 : such that f λ ( n ) 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 ( ) 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

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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 × 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

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In this work we give a characterization of the projective invariant pseudometric P , introduced by H. Wu, for a particular class of real 𝐂 -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 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

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In this work we give a characterization of the projective invariant pseudometric P , introduced by H. Wu, for a particular class of real 𝐂 -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 n , endowed with the characteristic metric.

Stacks of group representations

Paul Balmer (2015)

Journal of the European Mathematical Society

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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

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Let K be a field of characteristic p > 0, K* the multiplicative group of K and G = G p × 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...

Rings consisting entirely of certain elements

Huanyin Chen, Marjan Sheibani, Nahid Ashrafi (2018)

Czechoslovak Mathematical Journal

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We completely determine when a ring consists entirely of weak idempotents, units and nilpotents. We prove that such ring is exactly isomorphic to one of the following: a Boolean ring; 3 3 ; 3 B where B is a Boolean ring; local ring with nil Jacobson radical; M 2 ( 2 ) or M 2 ( 3 ) ; or the ring of a Morita context with zero pairings where the underlying rings are 2 or 3 .

Projective abelian Hopf algebras over a field

Andrzej Skowroński

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CONTENTSIntroduction............................................................................................................................................51. Cohen schemes.................................................................................................................................72. Projective abelian Hopf algebras......................................................................................................113. The structure of groups H o m ( 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

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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.

Characterizing projective general unitary groups PGU 3 ( q 2 ) by their complex group algebras

Farrokh Shirjian, Ali Iranmanesh (2017)

Czechoslovak Mathematical Journal

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Let G be a finite group. Let X 1 ( G ) be the first column of the ordinary character table of G . We will show that if X 1 ( G ) = X 1 ( PGU 3 ( q 2 ) ) , then G PGU 3 ( q 2 ) . As a consequence, we show that the projective general unitary groups PGU 3 ( q 2 ) are uniquely determined by the structure of their complex group algebras.