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

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.

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

Leonid F. Barannyk (2010)

Colloquium Mathematicae

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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.

On the representation theory of braid groups

Ivan Marin (2013)

Annales mathématiques Blaise Pascal

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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...

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

Peter Vassilev Danchev (2006)

Archivum Mathematicum

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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 N { 0 } such that | A / G | 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

Peter Vassilev Danchev (2007)

Archivum Mathematicum

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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...

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 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....

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

Michael Harris, Anthony Scholl (2001)

Journal of the European Mathematical Society

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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.