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The monoid of semisimple multiclasses of the group \(G=G_2(K)\). (Russian, English) Zbl 1052.20029

Zap. Nauchn. Semin. POMI 265, Pt. II, 202-221 (1999); translation in J. Math. Sci., New York 112, No. 4, 4355-4366 (2002).
A multiclass in a group \(G\) is the product \(M=C_1\cdots C_k=\{c_1\cdots c_k\mid c_i\in C_i\}\) of a finite sequence of conjugacy classes \(C_1,\dots,C_k\subset G\). Let \(G\) be a simple algebraic group and let \(M_{\text{cs}}(G)\) denote the set of all closures (in the Zariski topology) of the multiclasses in \(G\) generated by semisimple conjugacy classes. \(M_{\text{cs}}(G)\) is a commutative monoid with respect to the operation \(m_1m_2=\overline{m_1m_2}\), where \(\overline m\) is the closure of \(m\). N. L. Gordeev [J. Algebra 173, No. 3, 715-744 (1995; Zbl 0832.14037)] described the structure of the monoid \(M_{\text{cs}}(G)\) for the group \(G=\text{SL}_n(K)\), where \(K\) is an algebraically closed field of characteristic zero. In this paper the structure of \(M_{\text{cs}}(G)\) is described for the case \(G=G_2(K)\).

MSC:

20G15 Linear algebraic groups over arbitrary fields
20E45 Conjugacy classes for groups

Citations:

Zbl 0832.14037
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