Geodesic
$*$ -Subvarieties of the Variety Generated by $\left( {{M}_{2}}\left( \mathbb{K} \right),\,t \right)$
Canadian journal of mathematics, Tome 55 (2003) no. 1, pp. 42-63

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Let $\mathbb{K}$ be a field of characteristic zero, and $*\,=\,t$ the transpose involution for the matrix algebra ${{M}_{2}}\left( \mathbb{K} \right)$ . Let $\mathfrak{U}$ be a proper subvariety of the variety of algebras with involution generated by $\left( {{M}_{2}}\left( \mathbb{K} \right),\,* \right)$ . We define two sequences of algebras with involution ${{R}_{p}},\,{{S}_{q}}$ , where $p,\,q\,\in \,\mathbb{N}$ . Then we show that ${{T}_{*}}\left( \mathfrak{U} \right)$ and ${{T}_{*}}\left( {{R}_{p}}\oplus \,{{S}_{q}} \right)$ are $*$ -asymptotically equivalent for suitable $p,\,q$ .
DOI : 10.4153/CJM-2003-002-7
Mots-clés : 16R10, 16W10, 16R50, algebras with involution, asymptotic equivalence 
Benanti, Francesca; Vincenzo, Onofrio M. Di; Nardozza, Vincenzo. $*$ -Subvarieties of the Variety Generated by $\left( {{M}_{2}}\left( \mathbb{K} \right),\,t \right)$. Canadian journal of mathematics, Tome 55 (2003) no. 1, pp. 42-63. doi: 10.4153/CJM-2003-002-7
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