Homotopes of Quasi Jordan Algebras
The notion of quasi-Jordan algebras was originally proposed by R. Velasquez and R. Fellipe. Later, M. R. Bremner provided a modification called K-B quasi-Jordan algebras; these include all Jordan algebras and all dialgebras, and hence all associative algebras. Any quasi-Jordan algebra is special if it is isomorphic to a quasi-Jordan subalgebra of some dialgebras. Keeping in view the pivotal role of homotopes in the theory of Jordan algebras, we begin a study of the homotopes of quasi-Jordan algebras; among other related results, we show that the homotopes of any special quasi-Jordan algebra are special quasi-Jordan algebras and that the homotopes of a K-B quasi-Jordan algebra is a quasi-Jordan algebra. In the sequel, we also give some open problems.
We initiate a study of involutions in the setting of complex quasi Jordan algebras and discuss the notions of self-adjoint and unitary elements; besides other results, we also obtain a Russo-Dye…
The notion of quasi-Jordan algebras was originally proposed by R. Velasquez and R. Fellipe. Later, M. R. Bremner provided a modification called K-B quasi-Jordan algebras; these include all Jordan…
Idempotents play a basic role in the study of algebras. Peirce decomposition induced by an idempotent is
an important tool in the structure theory of non-associative algebras. In this note…