Isoclinism in Lie–Yamaguti algebras

A Lie–Yamaguti algebra is equipped with bilinear and trilinear operations. In this paper, we introduce the concept of isoclinism in Lie–Yamaguti algebras. From the definition of isoclinism, it is clear that isomorphism implies isoclinism, however the reverse may not be true. Further, we define a factor set for Lie–Yamaguti algebras and discuss some of its properties. By examining the factor set, we establish a condition under which the converse implication holds true for these algebras. In particular, we show that the notions of isoclinism and isomorphism are equivalent for two finite-dimensional Lie–Yamaguti algebras of the same dimension.