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Based on invariant algebras, we introduce representations6−th of Lie algebras and representationsh4−thi of Leibniz algebras, give the extended P-B-W Theorems in the context of the new repr...
Let g be a complex, semisimple Lie algebra. Drinfeld showed that the quantum loop algebra U~(Lg) of g degenerates to the Yangian Y~(g). We strengthen this result by constructing an explicit algebra ho...
We introduce P-graphs, which are generalisations of directed graphs in which paths have a degree in a semigroup P rather than a length in N. We focus on semigroups P arising as part of a quasi-lattice...
We study the problem of infinitesimal deformations of all real sim-ple finite-dimensional Filippov (or n-Lie) algebras considered as a class of n-Leibniz algebras characterized by having a n-bracket s...
We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and the...
We introduce the concept of weight of a planar algebra P and construct a new planar algebra referred as the perturbation of P by the weight. We establish a one-to-one correspondence between pivotal s...

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