Journal of Lie Theory 22 (2012), No. 2, 465--479
Copyright Heldermann Verlag 2012
On the Codimension Growth of Simple Color Lie Superalgebras
Dusan Pagon
Inst. of Mathematics, Physics and Mechanics, Faculty of Natural Sciences and Mathematics, University of Maribor, P. O. Box 2964, Ljubljana 1001, Slovenia
dusan.pagon@uni-mb.si
Dusan Repovs
Faculty of Mathematics and Physics, University of Ljubljana, P. O. Box 2964, Ljubljana 1001, Slovenia
dusan.repovs@guest.arnes.si
Mikhail Zaicev
Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow 119992, Russia
zaicevmv@mail.ru
We study polynomial identities of finite dimensional simple color Lie superalgebras over an algebraically closed field of characteristic zero graded by the product of two cyclic groups of order 2. We prove that the codimensions of identities grow exponentially and the rate of exponent equals the dimension of the algebra. A similar result is also obtained for graded identities and graded codimensions.
Keywords: Color Lie superalgebras, polynomial identities, codimensions, exponential growth.
MSC: 17B01, 17B75; 17B20
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