A Star-Variety With Almost Polynomial Growth

✍ Scribed by S. Mishchenko; A. Valenti

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 142 KB
• Volume: 223
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1999.8046

✦ Synopsis

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.