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A Star-Variety With Almost Polynomial Growth by S. Mishchenko; A. Valenti is a Mathematics article available to read on EtoBox.

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Let F be a field of characteristic zero. In this paper we construct a finite dimensional F-algebra with involution M and we study its )-polynomial identities; on one hand we determine a generator of the corresponding T-ideal of the free algebra with involution and on the other we give a complete description of the multilinear )-identities through the representation theory of the hyperoctahedral group. As an outcome of this study we show that the )-variety generated by M, Ž . var M, ) has almost polynomial growth, i.e., the sequence of )-codimensions of M cannot be bounded by any polynomial function but any proper )-subvariety of Ž . var M, ) has polynomial growth. If G is the algebra constructed in Giambruno 2 ## Ž . and Mishchenko preprint , we next prove that M and G are the only two finite 2 dimensional algebras with involution generating )-varieties with almost polynomial growth.

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Author

S. Mishchenko; A. Valenti

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0021-8693)

Published

2000

Language

EN

Field

Mathematics (Physical Sciences)