Gateaux Differentials in Banach Algebras.
Gelfand-Kirillor Dimension for non-Associative Algebras
General construction of Banach-Grassmann algebras
We show that a free graded commutative Banach algebra over a (purely odd) Banach space is a Banach-Grassmann algebra in the sense of Jadczyk and Pilch if and only if is infinite-dimensional. Thus, a large amount of new examples of separable Banach-Grassmann algebras arise in addition to the only one example previously known due to A. Rogers.
Generalized atypical supertableaux for superunitary and orthosymplectic groups
Generalized derivations of Lie triple systems
In this paper, we present some basic properties concerning the derivation algebra Der (T), the quasiderivation algebra QDer (T) and the generalized derivation algebra GDer (T) of a Lie triple system T, with the relationship Der (T) ⊆ QDer (T) ⊆ GDer (T) ⊆ End (T). Furthermore, we completely determine those Lie triple systems T with condition QDer (T) = End (T). We also show that the quasiderivations of T can be embedded as derivations in a larger Lie triple system.
Growth of some varieties of Leibniz-Poisson algebras
2010 Mathematics Subject Classification: 17A32, 17B63.Let V be a variety of Leibniz-Poisson algebras over an arbitrary field whose ideal of identities contains the identities {{x1,y1},{x2,y2},ј,{xm,ym}} = 0, {x1,y1}·{x2,y2}· ј ·{xm,ym} = 0 for some m. It is shown that the exponent of V exists and is an integer.