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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Zelevinski algebras related to projective representations

Authors: M. Bean and P. Hoffman
Journal: Trans. Amer. Math. Soc. 309 (1988), 99-111
MSC: Primary 20C25; Secondary 20C30
MathSciNet review: 957063
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Abstract: We define $ L$- $ \operatorname{PSH} $-algebras, and prove a classification theorem for such objects. The letters refer respectively to a ground ring $ L$ and to the positivity, selfadjointness and Hopf structures on an algebra, the basic example of which occurred in the study of projective representations of $ {S_n}$. This is analogous to an idea over $ {\mathbf{Z}}$ due to Zelevinski in connection with linear representations.

References [Enhancements On Off] (What's this?)

  • [H] P. Hoffman, $ \tau $-rings and wreath product representations, Lecture Notes in Math., vol. 746, Springer, 1979. MR 549031 (82d:55004)
  • [H-H1] Peter Hoffman and John Humphreys, Hopf algebras and projective representations of $ G\wr {S_n}$, and $ G\wr {A_n}$, Canad. J. Math. 38 (1986), 1380-1458. MR 873418 (88h:20014)
  • [H-H2] -, Projective representations of generalized symmetric groups using $ PSH$-algebras (to appear).
  • [L] A. Liulevicius, Arrows, symmetries and representation rings, J. Pure Appl. Algebra 19 (1980), 259-273. MR 593256 (82j:16020)
  • [Z] Andrey V. Zelevinski, Representations of finite classical groups, Lecture Notes in Math., vol. 869, Springer, 1981. MR 643482 (83k:20017)

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Article copyright: © Copyright 1988 American Mathematical Society

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