Abstract. For a given variety Var of algebras we define the variety Var of dialgebras. This construction turns to be closely related with varieties of pseudo-algebras: every Var-dialgebra can be embedded into an appropriate pseudo-algebra of the variety Var. In particular, Leibniz algebras are exactly Lie dialgebras, and every Leibniz algebra can be embedded into current Lie conformal algebra.

Abstract. We study the algebra of conformal endomorphisms Cend G,G n of a finitely generated free module Mn over the coordinate Hopf algebra H of a linear algebraic group G. It is shown that a conformal subalgebra of Cendn acting irreducibly on Mn generates an essential left ideal of Cend G,G n if enriched with operators of multiplication on elements of H. In particular, we describe such subalgebras for the case when G is finite. Introduction. The notion of a conformal algebra was introduced in [1] as a tool for investigation of vertex algebras [2, 3]. From the formal point of view, a conformal algebra is a linear space C over a field k (chark = 0) endowed with a linear operator T: C → C and with a family of bilinear operations ( · n ·), n ∈ Z+ (where Z+ stands for the set of non-negative integers), satisfying the following axioms:

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