Von-Neumann finiteness and reversibility in some classes of non-associative algebras
arXiv:1608.04898 · doi:10.1007/s10468-020-09988-4
Abstract
We investigate criteria for von-Neumann finiteness and reversibility in some classes of non-associative algebras. We show that all finite-dimensional alternative algebras, as well as all algebras obtained from the real numbers via the standard Cayley-Dickson doubling process, are von-Neumann finite. Precise criteria for von-Neumann finiteness and reversibility of involutive algebras are given, in terms of isomorphism types of their 3-dimensional subalgebras.
9 pages. Preliminary version