Research Article
Year 2020, Volume 28, Issue 28, 175 - 186, 14.07.2020

### 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, Volume 28, Issue 28, 175 - 186, 14.07.2020

### 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.

### Details

Primary Language English Mathematics Articles Pierre LANDROCK This is me (Primary Author) University of Jena Germany July 14, 2020 Year 2020, Volume 28, Issue 28

### Cite

 Bibtex @research article { ieja768246, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {1710 Sokak, No:41, Batikent/Ankara}, publisher = {Abdullah HARMANCI}, year = {2020}, volume = {28}, number = {28}, pages = {175 - 186}, doi = {10.24330/ieja.768246}, title = {ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS}, key = {cite}, author = {Landrock, Pierre} } APA Landrock, P. (2020). ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS . International Electronic Journal of Algebra , 28 (28) , 175-186 . DOI: 10.24330/ieja.768246 MLA Landrock, P. "ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS" . International Electronic Journal of Algebra 28 (2020 ): 175-186 Chicago Landrock, P. "ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS". International Electronic Journal of Algebra 28 (2020 ): 175-186 RIS TY - JOUR T1 - ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS AU - PierreLandrock Y1 - 2020 PY - 2020 N1 - doi: 10.24330/ieja.768246 DO - 10.24330/ieja.768246 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 175 EP - 186 VL - 28 IS - 28 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.768246 UR - https://doi.org/10.24330/ieja.768246 Y2 - 2022 ER - EndNote %0 International Electronic Journal of Algebra ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS %A Pierre Landrock %T ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS %D 2020 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 28 %N 28 %R doi: 10.24330/ieja.768246 %U 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 AMA Landrock P. ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS. IEJA. 2020; 28(28): 175-186. Vancouver Landrock P. ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS. International Electronic Journal of Algebra. 2020; 28(28): 175-186. IEEE P. Landrock , "ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS", International Electronic Journal of Algebra, vol. 28, no. 28, pp. 175-186, Jul. 2020, doi:10.24330/ieja.768246