# Partial Representations and Partial Group Algebras

@article{Dokuchaev1999PartialRA, title={Partial Representations and Partial Group Algebras}, author={Mikhailo Dokuchaev and Ruy Exel and Paolo Piccione}, journal={Journal of Algebra}, year={1999}, volume={226}, pages={505-532} }

Abstract The partial group algebra of a group G over a field K , denoted by K par ( G ), is the algebra whose representations correspond to the partial representations of G over K -vector spaces. In this paper we study the structure of the partial group algebra K par ( G ), where G is a finite group. In particular, given two finite abelian groups G 1 and G 2 , we prove that if the characteristic of K does not divide the order of G 1 , then K par ( G 1 ) is isomorphic to K par ( G 2 ) if and…

## 67 Citations

Isomorphisms of Partial Group Rings

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- 2016

We prove that if two finite groups G1 and G2 admit an isomorphism between their lattices of subgroups which preserves subgroup rings over a commutative ring K then the partial group rings Kpar G1 and…

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Given a subgroup H of a finite group G, we begin a systematic study of the partial representations of G that restrict to global representations of H. After adapting several results from [DEP00]…

On Strongly Associative Group Algebras

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- 2008

Given a partial action α of a group G on the group algebra FH, where H is a finite group and F is a field whose characteristic p divides the order of H, we investigate the associativity question of…

Associativity of crossed products by partial actions, enveloping actions and partial representations

- Mathematics
- 2002

Given a partial action a of a group G on an associative algebra A, we consider the crossed product A × α G. Using the algebras of multipliers, we generalize a result of Exel (1997) on the…

On finite degree partial representations of group

- Mathematics
- 2004

We establish a one-to-one correspondence between the irreducible finite degree partial rep tions of a groupG and the (usual) irreducible representations of certain ideals of a groupoid a constructed…

Dilations of partial representations of Hopf algebras

- MathematicsJ. Lond. Math. Soc.
- 2019

The notion of a dilation for a partial representation of a Hopf algebra, which in case the partial representation origins from a partial action coincides with the enveloping action, is introduced to study the interactions between partial and global representation theory.

On elementary domains of partial projective representations of groups

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- 2013

We characterize the finite groups containing only elementary domains of factor sets of partial projective representations. A condition for a finite subset A of a group G, which contains the unity of…

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