Back to Search
Start Over
Trace identities and almost polynomial growth
- Source :
- Journal of Pure and Applied Algebra 225 (2), 2021
- Publication Year :
- 2020
-
Abstract
- In this paper we study algebras with trace and their trace polynomial identities over a field of characteristic 0. We consider two commutative matrix algebras: $D_2$, the algebra of $2\times 2$ diagonal matrices and $C_2$, the algebra of $2 \times 2$ matrices generated by $e_{11}+e_{22}$ and $e_{12}$. We describe all possible traces on these algebras and we study the corresponding trace codimensions. Moreover we characterize the varieties with trace of polynomial growth generated by a finite dimensional algebra. As a consequence, we see that the growth of a variety with trace is either polynomial or exponential.<br />Comment: 14 pages
- Subjects :
- Mathematics - Rings and Algebras
16R10, 16R30, 16R50
Subjects
Details
- Database :
- arXiv
- Journal :
- Journal of Pure and Applied Algebra 225 (2), 2021
- Publication Type :
- Report
- Accession number :
- edsarx.2012.10991
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.jpaa.2020.106501