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Year 2023, , 126 - 151, 10.07.2023
https://doi.org/10.24330/ieja.1295669

Abstract

References

  • C. Bessenrodt, T. Holm and A. Zimmermann, Generalized Reynolds ideals for non-symmetric algebras, J. Algebra, 312 (2007), 985-994.
  • S. Brenner, The Socle of the Center of a Group Algebra, Dissertation, Friedrich-Schiller-Universitat Jena, 2022.
  • M. Chlebowitz, Uber Abschatzungen von Algebreninvarianten, Dissertation, Universitat Augsburg, 1991.
  • M. Chlebowitz and B. Kulshammer, Symmetric local algebras with a 5- dimensional center, Trans. Amer. Math. Soc., 329 (1992), 715-731.
  • R. J. Clarke, On the radical of the centre of a group algebra, J. Lond. Math. Soc. (2), 1 (1969), 565-572.
  • M. Deiml, Normalformen fur endlich-dimensionale Algebren und Anwendungen, Diplomarbeit, Universitat Augsburg, 1993.
  • K. Gerhard, Dimensionsabschatzung von symmetrischen Lokalen Algebren, Diplomarbeit, Universitat Augsburg, 1993.
  • S. Koshitani, A note on the radical of the centre of a group algebra, J. Lond. Math. Soc. (2), 18(2) (1978), 243-246.
  • B. Kulshammer, Symmetric local algebras and small blocks of finite groups, J. Algebra, 88(1) (1984), 190-195.
  • B. Kulshammer, Lectures on Block Theory, London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, 1991.
  • B. Kulshammer, Group-theoretical descriptions of ring-theoretical invariants of group algebras, in Representation Theory of Finite Groups and Finite- Dimensional Algebras (Bielefeld, 1991), Progr. in Math., Birkhauser, Basel, 95 (1991), 425-442.
  • B. Kulshammer, Centers and radicals of group algebras and blocks, Arch. Math., 114 (2020), 619-629.
  • P. Landrock, On the radical of the center of small symmetric local algebras, Int. Electron. J. Algebra, 28 (2020), 175-186.
  • P. Landrock and B. Sambale, On centers of blocks with one simple module, J. Algebra, 472 (2017), 339-368.
  • M. Linckelmann, The Block Theory of Finite Group Algebras, Vol. 1, London Mathematical Society Student Texts, 91, Cambridge University Press, Cambridge, 2018.
  • H. Nagao and Y. Tsushima, Representations of Finite Groups, Academic Press, Boston, MA, 1989.
  • T. Nakayama, On Frobeniusean algebras I, Ann. Math., 40 (1939), 611-633.
  • A. Skowronski and K. Yamagata, Frobenius Algebras I, European Mathematical Society Publishing House, Zurich, 2011.

Ideals in the center of symmetric algebras

Year 2023, , 126 - 151, 10.07.2023
https://doi.org/10.24330/ieja.1295669

Abstract

We study symmetric algebras $A$ over a field $F$ in which the Jacobson radical of the center of $A$, the socle of the center of $A$ or the Reynolds ideal of $A$ are ideals.

References

  • C. Bessenrodt, T. Holm and A. Zimmermann, Generalized Reynolds ideals for non-symmetric algebras, J. Algebra, 312 (2007), 985-994.
  • S. Brenner, The Socle of the Center of a Group Algebra, Dissertation, Friedrich-Schiller-Universitat Jena, 2022.
  • M. Chlebowitz, Uber Abschatzungen von Algebreninvarianten, Dissertation, Universitat Augsburg, 1991.
  • M. Chlebowitz and B. Kulshammer, Symmetric local algebras with a 5- dimensional center, Trans. Amer. Math. Soc., 329 (1992), 715-731.
  • R. J. Clarke, On the radical of the centre of a group algebra, J. Lond. Math. Soc. (2), 1 (1969), 565-572.
  • M. Deiml, Normalformen fur endlich-dimensionale Algebren und Anwendungen, Diplomarbeit, Universitat Augsburg, 1993.
  • K. Gerhard, Dimensionsabschatzung von symmetrischen Lokalen Algebren, Diplomarbeit, Universitat Augsburg, 1993.
  • S. Koshitani, A note on the radical of the centre of a group algebra, J. Lond. Math. Soc. (2), 18(2) (1978), 243-246.
  • B. Kulshammer, Symmetric local algebras and small blocks of finite groups, J. Algebra, 88(1) (1984), 190-195.
  • B. Kulshammer, Lectures on Block Theory, London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, 1991.
  • B. Kulshammer, Group-theoretical descriptions of ring-theoretical invariants of group algebras, in Representation Theory of Finite Groups and Finite- Dimensional Algebras (Bielefeld, 1991), Progr. in Math., Birkhauser, Basel, 95 (1991), 425-442.
  • B. Kulshammer, Centers and radicals of group algebras and blocks, Arch. Math., 114 (2020), 619-629.
  • P. Landrock, On the radical of the center of small symmetric local algebras, Int. Electron. J. Algebra, 28 (2020), 175-186.
  • P. Landrock and B. Sambale, On centers of blocks with one simple module, J. Algebra, 472 (2017), 339-368.
  • M. Linckelmann, The Block Theory of Finite Group Algebras, Vol. 1, London Mathematical Society Student Texts, 91, Cambridge University Press, Cambridge, 2018.
  • H. Nagao and Y. Tsushima, Representations of Finite Groups, Academic Press, Boston, MA, 1989.
  • T. Nakayama, On Frobeniusean algebras I, Ann. Math., 40 (1939), 611-633.
  • A. Skowronski and K. Yamagata, Frobenius Algebras I, European Mathematical Society Publishing House, Zurich, 2011.
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Sofia Brenner This is me

Burkhard Kulshammer This is me

Early Pub Date May 11, 2023
Publication Date July 10, 2023
Published in Issue Year 2023

Cite

APA Brenner, S., & Kulshammer, B. (2023). Ideals in the center of symmetric algebras. International Electronic Journal of Algebra, 34(34), 126-151. https://doi.org/10.24330/ieja.1295669
AMA Brenner S, Kulshammer B. Ideals in the center of symmetric algebras. IEJA. July 2023;34(34):126-151. doi:10.24330/ieja.1295669
Chicago Brenner, Sofia, and Burkhard Kulshammer. “Ideals in the Center of Symmetric Algebras”. International Electronic Journal of Algebra 34, no. 34 (July 2023): 126-51. https://doi.org/10.24330/ieja.1295669.
EndNote Brenner S, Kulshammer B (July 1, 2023) Ideals in the center of symmetric algebras. International Electronic Journal of Algebra 34 34 126–151.
IEEE S. Brenner and B. Kulshammer, “Ideals in the center of symmetric algebras”, IEJA, vol. 34, no. 34, pp. 126–151, 2023, doi: 10.24330/ieja.1295669.
ISNAD Brenner, Sofia - Kulshammer, Burkhard. “Ideals in the Center of Symmetric Algebras”. International Electronic Journal of Algebra 34/34 (July 2023), 126-151. https://doi.org/10.24330/ieja.1295669.
JAMA Brenner S, Kulshammer B. Ideals in the center of symmetric algebras. IEJA. 2023;34:126–151.
MLA Brenner, Sofia and Burkhard Kulshammer. “Ideals in the Center of Symmetric Algebras”. International Electronic Journal of Algebra, vol. 34, no. 34, 2023, pp. 126-51, doi:10.24330/ieja.1295669.
Vancouver Brenner S, Kulshammer B. Ideals in the center of symmetric algebras. IEJA. 2023;34(34):126-51.