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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...
Co-universal C*-algebras associated to generalised graphs
Higher rank graph co-universal algebra graph algebra Cuntz- Krieger algebra
2010/11/30
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...
On a class of n-Leibniz deformations of the simple Filippov algebras
n-Leibniz deformations simple Filippov algebras
2010/12/6
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...
Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
Supercharacters symmetric functions noncommuting variables related Hopf algebras
2010/12/9
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...