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,
Volume: 34 Issue: 34, 126 - 151, 10.07.2023
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.
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.
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.