Pseudoblocks of Finite Dimensional Algebras

Year 2020, Volume: 3 Issue: 1, 61 - 69, 10.06.2020

Afaf Alharthi , Ahmed Khammash

https://doi.org/10.33401/fujma.691602

Abstract

The notion of pseudoblocks is borrowed from [1] and introduced to finite-dimensional algebras. We determine the pseudoblocks for several known algebras such as the triangular algebra and the cyclic group algebra. Also, we determine the pseudoblocks for the group algebra of the special linear group $SL(2,p)$ in the natural characteristic being the only finite group of Lie type of finite representation type.

Keywords

Endomorphism algebra, Extensions, Hecke algebras, Modules, Pseudoblocks, Representations, Tensor algebras

References

• [1] A. Khammash, The pseudoblocks of endomorphism algebras, Int. Math. Forum, 4(48) (2009), 2363-2368.
• [2] J. Alperin, Local Representation Theory: Modular Representations as an Introduction to the Local Representation Theory of Finite Groups, Cambridge University Press, 1986.
• [3] A. Khammash, Brauer-fitting correspondence on tensor algebra, Int. J. Algebra, 8(19) (2014), 895-901.
• [4] K. Erdmann, T. Holm, Algebras and Representation Theory, Springer, 2018.
• [5] J. Humphreys, Modular Representations of Finite Groups of Lie Type, Cambridge University Press, 2006.
• [6] L. Dornhoff, Group Representation Theory: Modular Representation Theory, M. Dekker, 1972.
• [7] D. Craven, Maximal psl2 subgroups of exceptional groups of lie type, (2019), arXiv:1610.07469.