arXiv subjects

Harry Petyt

Publications and source records attributed to Harry Petyt.

20 records · Page 2Linked to original sources

arXiv2020

Derivations of octonion matrix algebras

It is well-known that the exceptional Lie algebras $\mathfrak{f}_4$ and $\mathfrak{g}_2$ arise from the octonions as the derivation algebras of the $3\times3$ hermitian and $1\times1$ antihermitian matrices, respectively. Inspired by this, we compute the derivation algebras of the spaces of hermitian and antihermitian matrices over an octonion algebra in all dimensions.

math.RA↗

arXiv2019

The special linear group for nonassociative rings

We extend to arbitrary rings a definition of the octonion special linear group due to Baez. At the infinitesimal level we get a Lie ring, which we describe over some large classes of rings, including all associative rings and all algebras over a field. As a corollary we compute all the groups Baez defined.

math.RA↗