Combinaisons non-associatives
Commentary to: Generalized derivations of Lie triple systems
Commutator algebras arising from splicing operations
We prove that the variety of Lie algebras arising from splicing operation coincides with the variety CM of centreby-metabelian Lie algebras. Using these Lie algebras we find the minimal dimension algebras generated the variety CM and the variety of its associative envelope algebras. We study the splicing n-ary operation. We show that all n-ary (n > 2) commutator algebras arising from this operation are nilpotent of index 3. We investigate the generalization of the splicing n-ary operation, and...
Composition-diamond lemma for modules
We investigate the relationship between the Gröbner-Shirshov bases in free associative algebras, free left modules and “double-free” left modules (that is, free modules over a free algebra). We first give Chibrikov’s Composition-Diamond lemma for modules and then we show that Kang-Lee’s Composition-Diamond lemma follows from it. We give the Gröbner-Shirshov bases for the following modules: the highest weight module over a Lie algebra , the Verma module over a Kac-Moody algebra, the Verma module...
Conditional Expectation and Bicontractive Projections on Jordan C*-algebras and Their Generalizations.
Conformal representations of Leibniz algebras.
Congruences and ideals in ternary rings
A ternary ring is an algebraic structure of type satisfying the identities and where, moreover, for any , , there exists a unique with . A congruence on is called normal if is a ternary ring again. We describe basic properties of the lattice of all normal congruences on and establish connections between ideals (introduced earlier by the third author) and congruence kernels.
Conservative algebras and superalgebras: a survey
We give a survey of results obtained on the class of conservative algebras and superalgebras, as well as on their important subvarieties, such as terminal algebras.
Construction of countable ternary rings of suitable types [Abstract of thesis]
Construction of Nijenhuis operators and dendriform trialgebras.
Contributions to the theory of (1,1) rings
Corrigendum to: “A concrete analysis of the radical concept".
CUP-Product for Leibnitz Cohomology and Dual Leibniz Algebras.