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Year 2020, , 175 - 186, 14.07.2020
https://doi.org/10.24330/ieja.768246

Abstract

References

  • M. Chlebowitz and B. Külshammer, Symmetric local algebras with 5-dimensional center, Trans. Amer. Math. Soc., 329(2) (1992), 715-731.
  • T. C. Craven and T. L. Smith, Symmetric algebras over rings and fields, Bull. Aust. Math. Soc., 89(3) (2014), 466-472.
  • C. W. Eaton, Morita equivalence classes of blocks with elementary abelian defect groups of order 16, preprint, arXiv:1612.03485v4, (2019).
  • 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. Lond. Math. Soc., 85(2) (2012), 491-510.
  • B. Külshammer, Symmetric local algebras and small blocks of finite groups, J. Algebra, 88 (1984), 190-195.
  • P. Landrock, Eine Klasse von Blocken mit Einer Elementarabelschen Defektgruppe der Ordnung 16, Ph.D. Thesis, Jena 2018.
  • P. Landrock and B. Sambale, On centers of blocks with one simple module, J. Algebra, 472 (2017), 339-368.

ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS

Year 2020, , 175 - 186, 14.07.2020
https://doi.org/10.24330/ieja.768246

Abstract

This article is motivated by some results from Chlebowitz and Külshammer on how the structure of a symmetric local algebra is influenced by its center. They have shown that a symmetric local algebra is almost always commutative if its center is at most 5-dimensional. In this article we are interested in how the ideal property of the radical of the center of a symmetric local algebra is influenced by the dimension of the algebra itself. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$

References

  • M. Chlebowitz and B. Külshammer, Symmetric local algebras with 5-dimensional center, Trans. Amer. Math. Soc., 329(2) (1992), 715-731.
  • T. C. Craven and T. L. Smith, Symmetric algebras over rings and fields, Bull. Aust. Math. Soc., 89(3) (2014), 466-472.
  • C. W. Eaton, Morita equivalence classes of blocks with elementary abelian defect groups of order 16, preprint, arXiv:1612.03485v4, (2019).
  • 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. Lond. Math. Soc., 85(2) (2012), 491-510.
  • B. Külshammer, Symmetric local algebras and small blocks of finite groups, J. Algebra, 88 (1984), 190-195.
  • P. Landrock, Eine Klasse von Blocken mit Einer Elementarabelschen Defektgruppe der Ordnung 16, Ph.D. Thesis, Jena 2018.
  • P. Landrock and B. Sambale, On centers of blocks with one simple module, J. Algebra, 472 (2017), 339-368.
There are 7 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Pierre Landrock This is me

Publication Date July 14, 2020
Published in Issue Year 2020

Cite

APA Landrock, P. (2020). ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS. International Electronic Journal of Algebra, 28(28), 175-186. https://doi.org/10.24330/ieja.768246
AMA Landrock P. ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS. IEJA. July 2020;28(28):175-186. doi:10.24330/ieja.768246
Chicago Landrock, Pierre. “ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS”. International Electronic Journal of Algebra 28, no. 28 (July 2020): 175-86. https://doi.org/10.24330/ieja.768246.
EndNote Landrock P (July 1, 2020) ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS. International Electronic Journal of Algebra 28 28 175–186.
IEEE P. Landrock, “ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS”, IEJA, vol. 28, no. 28, pp. 175–186, 2020, doi: 10.24330/ieja.768246.
ISNAD Landrock, Pierre. “ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS”. International Electronic Journal of Algebra 28/28 (July 2020), 175-186. https://doi.org/10.24330/ieja.768246.
JAMA Landrock P. ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS. IEJA. 2020;28:175–186.
MLA Landrock, Pierre. “ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS”. International Electronic Journal of Algebra, vol. 28, no. 28, 2020, pp. 175-86, doi:10.24330/ieja.768246.
Vancouver Landrock P. ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS. IEJA. 2020;28(28):175-86.

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