Definition 1.1. A curved L∞ algebra over A consists of a locally free finitely generated graded A]-module V, together with a cohomological degree 1 and square zero derivation d : Ŝym(V∨[−1])→ Ŝym(V∨[−1]) where V∨ is the A]-linear dual and the completed symmetric algebra is also over A]. There are two additional requirements on the derivation d: (1) The derivation d makes Ŝym(V∨[−1]) into a dga ...

In the present paper, we study simple algebras, which do not belong to well-known classes of algebras (associative alternative Lie Jordan etc.). The finite-dimensional over a field characteristic 0 without finite basis identities, constructed by Kislitsin, are such algebras. consider two algebras: seven-dimensional anticommutative algebra \(\mathcal{D}\) and central commutative \(\mathcal{C}\)....

In this article, we introduce equivariant formal deformation theory of Lie triple systems. We an cohomology systems and using study the

I show that the projective Schur functions may be interpreted as bispherical functions of either the triple (q(n), q(n)⊕q(n), q(n)), where q(n) is the “odd” (queer) analog of the general linear Lie algebra, or the triple (pe(n), gl(n|n), pe(n)), where pe(n) is the periplectic Lie superalgebra which preserves the nondegenerate odd bilinear form (either symmetric or skew-symmetric). Making use of...