3-dimensional Griess Algebras and Miyamoto Involutions

Involutions of 3-dimensional Handlebodies

We study the orientation preserving involutions of the orientable 3-dimensional handlebody Hg, for any genus g. A complete classification of such involutions is given in terms of their fixed points.

Algebras and Involutions

• Vectorspaces over division rings • Matrices, opposite rings • Semi-simple modules and rings • Semi-simple algebras • Reduced trace and norm • Other criteria for simplicity • Involutions • Brauer group of a field • Tensor products of fields • Crossed product construction of simple algebras • Cyclic algebra construction of simple algebras • Quaternion algebras • Examples • Unramified extensions...

Se p 20 02 Vertex operator algebra with two Miyamoto involutions generating S 3 Shinya Sakuma

In this article we study a VOA with two Miyamoto involutions generating S3. In [M3], Miyamoto showed that a VOA generated by two conformal vectors whose Miyamoto involutions generate an automorphism group isomorphic to S3 is isomorphic to one of the four candidates he listed. We construct one of them and prove that our VOA is actually the same as VA(e, f) studied by Miyamoto. We also show that ...

Involutions of reductive Lie algebras

Let G be a reductive group over a field of characteristic 6= 2, let g = Lie(G), let θ be an involutive automorphism of G and let g = k⊕p be the associated symmetric space decomposition. For k = C, Kostant and Rallis studied [17] properties of orbits, centralizers, and invariants related to the (−1) eigenspace p. In this paper, we generalise [17] to the case of good positive characteristic. Amon...

Involutions on graded matrix algebras