On the Cayley degree of an algebraic group
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
Penulis (3)
N. Lemire
V. Popov
Z. Reichstein
Akses Cepat
PDF tidak tersedia langsung
Cek di sumber asli →- Tahun Terbit
- 2006
- Bahasa
- en
- Total Sitasi
- 2×
- Sumber Database
- Semantic Scholar
- Akses
- Open Access ✓