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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Irreducible representations of solvable Lie superalgebras
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by Alexander Sergeev
Represent. Theory 3 (1999), 435-443
DOI: https://doi.org/10.1090/S1088-4165-99-00086-2
Published electronically: November 9, 1999
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Abstract:

The description of irreducible finite dimensional representations of finite dimensional solvable Lie superalgebras over complex numbers given by V. Kac is refined. In reality these representations are not just induced from a polarization but are twisted ones, as infinite dimensional representations of solvable Lie algebras. Various cases of irreducibility (general and of type Q) are classified.
References
  • J. N. Bernstein and D. A. Leĭtes, The superalgebra $Q(n)$, the odd trace and the odd determinant, C. R. Acad. Bulgare Sci. 35 (1982), no. 3, 285–286. MR 677839
  • Jacques Dixmier, Enveloping algebras, Graduate Studies in Mathematics, vol. 11, American Mathematical Society, Providence, RI, 1996. Revised reprint of the 1977 translation. MR 1393197, DOI 10.1090/gsm/011
  • V. G. Kac, Lie superalgebras, Advances in Math. 26 (1977), no. 1, 8–96. MR 486011, DOI 10.1016/0001-8708(77)90017-2
  • Leites D. (ed.), Seminar on supermanifolds #22, Reports of the Department of Mathematics of Stockholm University, 1988-4, 1–12.
  • I. M. Shchepochkina, Maximal solvable subalgebras of the Lie superalgebras $\textrm {gl}(m|n)$ and $\textrm {sl}(m|n)$, Funktsional. Anal. i Prilozhen. 28 (1994), no. 2, 92–94 (Russian); English transl., Funct. Anal. Appl. 28 (1994), no. 2, 147–149. MR 1283268, DOI 10.1007/BF01076514
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Bibliographic Information
  • Alexander Sergeev
  • Affiliation: On leave of absence from Balakovo Institute of Technique of Technology and Control, Branch of Saratov State Technical University, Russia; Department of Mathematics, University of Stockholm, Roslagsv. 101, Kräftriket hus 6, S-106 91, Stockholm, Sweden
  • Email: mleites@matematik.su.se (subject: for Sergeev)
  • Received by editor(s): November 4, 1998
  • Received by editor(s) in revised form: September 8, 1999
  • Published electronically: November 9, 1999
  • © Copyright 1999 American Mathematical Society
  • Journal: Represent. Theory 3 (1999), 435-443
  • MSC (1991): Primary 17A70; Secondary 17B30
  • DOI: https://doi.org/10.1090/S1088-4165-99-00086-2
  • MathSciNet review: 1722111