arXiv Open Access 2006

On the Cayley degree of an algebraic group

Nicole Lemire Vladimir L. Popov Zinovy Reichstein

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Abstrak

A connected linear algebraic group G is called a Cayley group if the Lie algebra of G endowed with the adjoint G-action and the group variety of G endowed with the conjugation G-action are birationally G-isomorphic. In particular, the classical Cayley map, X \mapsto (I_n-X)/(I_n+X), between the special orthogonal group SO_n and its Lie algebra so_n, shows that SO_n is a Cayley group. In an earlier paper (see math.AG/0409004) we classified the simple Cayley groups defined over an algebraically closed field of characteristic zero. Here we consider a new numerical invariant of G, the Cayley degree, which "measures" how far G is from being Cayley, and prove upper bounds on Cayley degrees of some groups.

Topik & Kata Kunci

math.AG math.GR

Penulis (3)

Nicole Lemire

Vladimir L. Popov

Zinovy Reichstein

Format Sitasi

APA MLA BibTeX

Lemire, N., Popov, V.L., Reichstein, Z. (2006). On the Cayley degree of an algebraic group. https://arxiv.org/abs/math/0608473

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2006
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓