Separable deformations of the generalized quaternion group algebras

Author:

Ginosar Yuval1

Affiliation:

1. Department of Mathematics , University of Haifa , Haifa 31905 , Israel

Abstract

Abstract The group algebras k Q 2 n {kQ_{2^{n}}} of the generalized quaternion groups Q 2 n {Q_{2^{n}}} over fields k which contain 𝔽 2 n - 2 {\mathbb{F}_{2^{n-2}}} are deformed to separable k ( ( t ) ) {k((t))} -algebras [ k Q 2 n ] t {[kQ_{2^{n}}]_{t}} . The dimensions of the simple components of k ( ( t ) ) ¯ k ( ( t ) ) [ k Q 2 n ] t {\overline{k((t))}\otimes_{k((t))}[kQ_{2^{n}}]_{t}} over the algebraic closure k ( ( t ) ) ¯ {\overline{k((t))}} , and those of Q 2 n {\mathbb{C}Q_{2^{n}}} over {\mathbb{C}} are the same, yielding strong solutions of the Donald–Flanigan conjecture for the generalized quaternion groups.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Reference13 articles.

1. N. Barnea and Y. Ginosar, A separable deformation of the quaternion group algebra, Proc. Amer. Math. Soc. 136 (2008), no. 8, 2675–2681.

2. J. D. Donald and F. J. Flanigan, A deformation-theoretic version of Maschke’s theorem for modular group algebras: The commutative case, J. Algebra 29 (1974), 98–102.

3. K. Erdmann, On semisimple deformations of local semidihedral algebras, Arch. Math. (Basel) 63 (1994), no. 6, 481–487.

4. K. Erdmann and M. Schaps, Deformation of tame blocks and related algebras, Quantum Deformations of Algebras and Their Representations (Ramat-Gan, Rehovot 1991/1992), Israel Math. Conf. Proc. 7, Bar-Ilan University, Ramat Gan (1993), 25–44.

5. M. Gerstenhaber and A. Giaquinto, Compatible deformations, Trends in the Representation Theory of Finite-dimensional Algebras (Seattle 1997), Contemp. Math. 229, American Mathematical Society, Providence (1998), 159–168.

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1. An inductive method for separable deformations;The Quarterly Journal of Mathematics;2024-05-16

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