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Search: MSC category 16R50 ( Other kinds of identities (generalized polynomial, rational, involution) )

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1. CJM 2003 (vol 55 pp. 42)

Benanti, Francesca; Di Vincenzo, Onofrio M.; Nardozza, Vincenzo
$*$-Subvarieties of the Variety Generated by $\bigl( M_2(\mathbb{K}),t \bigr)$
Let $\mathbb{K}$ be a field of characteristic zero, and $*=t$ the transpose involution for the matrix algebra $M_2 (\mathbb{K})$. Let $\mathfrak{U}$ be a proper subvariety of the variety of algebras with involution generated by $\bigl( M_2 (\mathbb{K}),* \bigr)$. We define two sequences of algebras with involution $\mathcal{R}_p$, $\mathcal{S}_q$, where $p,q \in \mathbb{N}$. Then we show that $T_* (\mathfrak{U})$ and $T_* (\mathcal{R}_p \oplus \mathcal{S}_q)$ are $*$-asymptotically equivalent for suitable $p,q$.

Keywords:algebras with involution, asymptotic equivalence
Categories:16R10, 16W10, 16R50

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