Grading Structure for Derivations of Group Algebras

Authors

  • Andronick Arutyunov V.A. Trapeznikov Institute of Control Sciences Russian Academy of Sciences, Moscow, Russia
  • Igor Zhiltsov

DOI:

https://doi.org/10.25728/assa.2025.2025.1.2028

Keywords:

derivations, bimodule, outer derivations, graded algebras

Abstract

In this paper we give a way of equipping the derivation algebra of a group algebra with the structure of a graded algebra. The derived group is used as the grading group. For the proof, the identification of the derivation with the characters of the adjoint action groupoid is used. These results also allow us to obtain the analogous structure of a graded algebra for outer derivations. A non-trivial graduation is obtained for all groups that are not perfect.

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Published

2025-08-24

How to Cite

Grading Structure for Derivations of Group Algebras. (2025). Advances in Systems Science and Applications, 2025(1), 108-119. https://doi.org/10.25728/assa.2025.2025.1.2028