Tensor product of evolution algebras

Tensor product of finite dimensional nilpotent evolution algebras

“…Otherwise we say that E is tensorially indecomposable. [40] Proposition 2.4. [40] If E 1 and E 2 are evolution K-algebras, then E 1 ⊗ E 2 is also an evolution K-algebra.…”

“…[40] Proposition 2.4. [40] If E 1 and E 2 are evolution K-algebras, then E 1 ⊗ E 2 is also an evolution K-algebra. Furthermore, if B 1 = {e i } i∈Λ be a natural basis of E 1 and let B 2 = {f j } j∈Γ be a natural basis of E 2 , then {e i ⊗ f j } i∈Λ,j∈Γ is a natural basis of…”

“…Definition 2.2. [40] Let E 1 and E 2 be two K−algebras with bases {e i } i∈Λ and {f j } j∈Γ respectively. We define a product on E 1 ⊗ E 2 as follows:…”

“…Definition 2.3. [40] We say that a K-algebra E is tensorially decomposable if it is isomorphic to E 1 ⊗ E 2 where E 1 and E 2 are K-algebras with dim(E 1 ), dim(E 2 ) > 1. Otherwise we say that E is tensorially indecomposable.…”

“…The relation of evolution algebra and other kinds of non-associative algebras has been established [17]. Recently, in [40] the tensor product of evolution algebras has been defined and studied for the inheritance of properties from the tensor product to the factor and conversely. For instance, non-degeneracy, irreducibility, perfectness, and simplicity were investigated.…”