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

Leonid F. Barannyk

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Displaying similar documents to “On faithful projective representations of finite abelian p-groups over a field of characteristic p”

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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.

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

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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.

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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 $_{}$ .

On the representation theory of braid groups

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This work presents an approach towards the representation theory of the braid groups $B_{n}$ . We focus on finite-dimensional representations over the field of Laurent series which can be obtained from representations of infinitesimal braids, with the help of Drinfeld associators. We set a dictionary between representation-theoretic properties of these two structures, and tools to describe the representations thus obtained. We give an explanation for the frequent apparition of unitary structures...

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A note on the countable extensions of separable $p^{ω + n}$ -projective abelian $p$ -groups

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It is proved that if $G$ is a pure $p^{ω + n}$ -projective subgroup of the separable abelian $p$ -group $A$ for $n \in N \cup {0}$ such that $| A / G | \leq ℵ_{0}$ , then $A$ is $p^{ω + n}$ -projective as well. This generalizes results due to Irwin-Snabb-Cutler (CommentṀathU̇nivṠtṖauli, 1986) and the author (Arch. Math. (Brno), 2005).

On countable extensions of primary abelian groups

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It is proved that if $A$ is an abelian $p$ -group with a pure subgroup $G$ so that $A / G$ is at most countable and $G$ is either $p^{ω + n}$ -totally projective or $p^{ω + n}$ -summable, then $A$ is either $p^{ω + n}$ -totally projective or $p^{ω + n}$ -summable as well. Moreover, if in addition $G$ is nice in $A$ , then $G$ being either strongly $p^{ω + n}$ -totally projective or strongly $p^{ω + n}$ -summable implies that so is $A$ . This generalizes a classical result of Wallace (J. Algebra, 1971) for totally projective $p$ -groups as well as continues our recent investigations...

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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 $G = G_{p} \times B$ 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 abelian Hopf algebras over a field

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

A note on trilinear forms for reducible representations and Beilinson's conjectures

Michael Harris, Anthony Scholl (2001)

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We extend Prasad’s results on the existence of trilinear forms on representations of $G L_{2}$ of a local field, by permitting one or more of the representations to be reducible principal series, with infinite-dimensional irreducible quotient. We apply this in a global setting to compute (unconditionally) the dimensions of the subspaces of motivic cohomology of the product of two modular curves constructed by Beilinson.