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$*$-Subvarieties of the Variety Generated by $\bigl( M_2(\mathbb{K}),t \bigr)$

  Published:2003-02-01
 Printed: Feb 2003
  • Francesca Benanti
  • Onofrio M. Di Vincenzo
  • Vincenzo Nardozza
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Abstract

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 algebras with involution, asymptotic equivalence
MSC Classifications: 16R10, 16W10, 16R50 show english descriptions $T$-ideals, identities, varieties of rings and algebras
Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx]
Other kinds of identities (generalized polynomial, rational, involution)
16R10 - $T$-ideals, identities, varieties of rings and algebras
16W10 - Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx]
16R50 - Other kinds of identities (generalized polynomial, rational, involution)
 

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