Equivalence of -algebras for abelian

Author:
Alexandre Turull

Journal:
Proc. Amer. Math. Soc. **123** (1995), 1655-1660

MSC:
Primary 20C15

MathSciNet review:
1249894

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Abstract | References | Similar Articles | Additional Information

Abstract: We describe the equivalence classes of central simple *G*-algebras over an infinite field *F* for *G* a finite abelian group, provided the following holds. For each prime *p* for which the field *F* has primitive *p*th roots, the Sylow *p*-subgroup of *G* is either cyclic or elementary abelian.

**[1]**T. Y. Lam,*The algebraic theory of quadratic forms*, W. A. Benjamin, Inc., Reading, Mass., 1973. Mathematics Lecture Note Series. MR**0396410****[2]**Alexandre Turull,*The Schur index of projective characters of symmetric and alternating groups*, Ann. of Math. (2)**135**(1992), no. 1, 91–124. MR**1147958**, 10.2307/2946564**[3]**Alexandre Turull,*Clifford theory with Schur indices*, J. Algebra**170**(1994), no. 2, 661–677. MR**1302862**, 10.1006/jabr.1994.1359**[4]**Alexandre Turull,*Some invariants for equivalent 𝐺-algebras*, J. Pure Appl. Algebra**98**(1995), no. 2, 209–222. MR**1319970**, 10.1016/0022-4049(94)00032-E**[5]**Alexandre Turull,*Equivalence of 𝐺-algebras with complemented centroid*, Comm. Algebra**22**(1994), no. 12, 5037–5078. MR**1285725**, 10.1080/00927879408825120

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1995-1249894-9

Keywords:
Brauer group,
*G*-algebra,
finite groups,
representations

Article copyright:
© Copyright 1995
American Mathematical Society