Abstract
We introduce the notion of endomorph E(A) of a (super) algebra E(A) and prove thatE(A) is a simple (super) algebraif A is not an algebra of scalar multiplication.If A is a right-symmetric (super)algebra then E(A) is right-symmetric as well.Thus, we construct a wide class of simple(right-symmetric) (super)algebras which contains a matrix subalgebra with a common unity.We calculate the derivation algebra of the endomorphof a unital algebra A and the automorphism groupof the simple right-symmetric algebra E(Vn) (the endomorph of a direct sum of fields).
| Original language | English |
|---|---|
| Pages (from-to) | 859-866 |
| Number of pages | 8 |
| Journal | Siberian Mathematical Journal |
| Volume | 61 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 1 Sep 2020 |
Keywords
- 512.57
- automorphism
- derivation
- endomorph
- left-symmetric algebra
- pre-Lie algebra
- right-symmetric algebra
- simple algebra