Cayley groups

By N. Lemire, V. Popov, Zinovy Reichstein. 2004

50 citations recorded by the source corpus.

The classical Cayley map, X -->(I_n-X)/(I_n+X), is a birational isomorphism between the special orthogonal group SO_n and its Lie algebra so_n, which is SO_n-equivariant with respect to the conjugating and adjoint actions respectively. We ask whether or not maps with these properties can be constructed for other algebraic groups. We show that the answer is usually"no", with a few exceptions. In particular, we show that a Cayley map for the group SL_n exists if and only if n<= 3. This answers an old question of Luna.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/46d52ba58c53de034e4ed15761e5b0da43f31846

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Finite Subgroups of the Plane Cremona Group (2006, background): “ 6. One of the groups from this case, namely G ∼=2 ×S3 was considered in [40], [41] (the papers also discuss the relation of this problem to some questions in the theory of algebraic groups raised in [44]). It is proved there that (S,G) is not birationally isomorphic to (P2,G) but birationally isomo”
Jordan groups and automorphism groups of algebraic varieties (2013, background): “the ﬁrst and the second case. Since P and T are rational, these actions of G on P and T determine, up to conjugacy, resp., the subgroups GP and GT of Cr 2, both isomorphic to G. By [Is2003] (see also [LPR2006], [LPR2007]), these subgroups are not conjugate in Cr 2. However, by [LPR2007, Sect. 5], GT”