Research Article
Year 2018,
Volume: 23 Issue: 23, 1 - 24, 11.01.2018
Abstract
References
- J. L. Alperin and L. Evens, Representations, resolutions and Quillen’s dimension theorem, J. Pure Appl. Algebra, 22(1) (1981), 1-9.
- L. Héthelyi, E. Horváth, B. Külshammer and J. Murray, Central ideals and Cartan invariants of symmetric algebras, J. Algebra, 293(1) (2005), 243-260.
- R. Kessar, On blocks stably equivalent to a quantum complete intersection of dimension 9 in characteristic 3 and a case of the abelian defect group conjecture, J. London Math. Soc., 85(2) (2012), 491-510.
- M. Kiyota, On 3-blocks with an elementary abelian defect group of order 9, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 31(1) (1984), 33-58.
- B. Külshammer, Bemerkungen über die Gruppenalgebra als symmetrische Algebra II, J. Algebra, 75(1) (1982), 59-69.
- B. Külshammer, Symmetric local algebras and small blocks of finite groups, J. Algebra, 88(1) (1984), 190-195.
- B. Külshammer, Crossed products and blocks with normal defect groups, Comm. Algebra, 13(1) (1985), 147-168.
- B. Külshammer, Group-theoretical descriptions of ring-theoretical invariants of group algebras, in Representation theory of finite groups and finite-dimensional algebras (Bielefeld, 1991), Progr. Math., 95, Birkhäuser, Basel, (1991), 425- 442.
- B. Külshammer, Lectures on Block Theory, London Mathematical Society Lecture Note Series, 161, Cambridge University Press, Cambridge, 1991.
- L. Puig and Y. Usami, Perfect isometries for blocks with abelian defect groups and Klein four inertial quotients, J. Algebra, 160(1) (1993), 192-225.
- S. Reinhardt, Eine Klasse von 3-Blöcken mit Defekt 2, Master’s thesis, Jena 2015.
Year 2018,
Volume: 23 Issue: 23, 1 - 24, 11.01.2018
Abstract
Motivated by a problem concerning the structure of certain 3-
blocks of defect 2 in finite groups we investigate a class of local algebras of
dimension 9 over a field of characteristic 3. In particular, we compute the
complexity of the unique simple module for any such algebra.
Keywords
References
- J. L. Alperin and L. Evens, Representations, resolutions and Quillen’s dimension theorem, J. Pure Appl. Algebra, 22(1) (1981), 1-9.
- L. Héthelyi, E. Horváth, B. Külshammer and J. Murray, Central ideals and Cartan invariants of symmetric algebras, J. Algebra, 293(1) (2005), 243-260.
- R. Kessar, On blocks stably equivalent to a quantum complete intersection of dimension 9 in characteristic 3 and a case of the abelian defect group conjecture, J. London Math. Soc., 85(2) (2012), 491-510.
- M. Kiyota, On 3-blocks with an elementary abelian defect group of order 9, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 31(1) (1984), 33-58.
- B. Külshammer, Bemerkungen über die Gruppenalgebra als symmetrische Algebra II, J. Algebra, 75(1) (1982), 59-69.
- B. Külshammer, Symmetric local algebras and small blocks of finite groups, J. Algebra, 88(1) (1984), 190-195.
- B. Külshammer, Crossed products and blocks with normal defect groups, Comm. Algebra, 13(1) (1985), 147-168.
- B. Külshammer, Group-theoretical descriptions of ring-theoretical invariants of group algebras, in Representation theory of finite groups and finite-dimensional algebras (Bielefeld, 1991), Progr. Math., 95, Birkhäuser, Basel, (1991), 425- 442.
- B. Külshammer, Lectures on Block Theory, London Mathematical Society Lecture Note Series, 161, Cambridge University Press, Cambridge, 1991.
- L. Puig and Y. Usami, Perfect isometries for blocks with abelian defect groups and Klein four inertial quotients, J. Algebra, 160(1) (1993), 192-225.
- S. Reinhardt, Eine Klasse von 3-Blöcken mit Defekt 2, Master’s thesis, Jena 2015.
There are 11 citations in total.
Details
| Journal Section | Research Article |
|---|---|
| Authors | |
| Publication Date | January 11, 2018 |
| DOI | https://doi.org/10.24330/ieja.373631 |
| IZ | https://izlik.org/JA69CZ69KD |
| Published in Issue | Year 2018 Volume: 23 Issue: 23 |