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Algebraic bivariant K-theory and Leavitt path algebras
(European Mathematical Society, 2021-02-02)
We investigate to what extent homotopy invariant, excisive and matrix stable homology theories help one distinguish between the Leavitt path algebras L.E/ and L.F / of graphs E and F over a commutative ground ring `. We ...
Lie structure on the Hochschild cohomology of a family of subalgebras of the Weyl algebra
(European Mathematical Society, 2021-12-07)
For each nonzero h ∈ F[x], where F is a field, let Ah be the unital associative algebra generated by elements x; y, satisfying the relation yx - xy = h. This gives a parametric family of subalgebras of the Weyl algebra A1, ...
On the structure of (co-Frobenius) Hopf algebras
(European Mathematical Society, 2013-03)
We introduce a new filtration on Hopf algebras, the standard filtration, generalizing the coradical filtration. Its zeroth term, called the Hopf coradical, is the subalgebra generated by the coradical. We give a structure ...
PBW-deformations and deformations à la Gerstenhaber of N-Koszul algebras
(European Mathematical Society, 2014-07)
In this article we establish an explicit link between the classical theory of deformations à la Gerstenhaber (and a fortiori with the Hochschild cohomology) and (weak) PBW-deformations of homogeneous algebras. Our point ...
Quantum function algebras from finite-dimensional Nichols algebras
(European Mathematical Society, 2020-10)
We describe how to find quantum determinants and antipode formulas from braidedvector spaces using the FRT-construction and finite-dimensional Nichols algebras. It improvesthe construction of quantum function algebras using ...
On weakly group-theoretical non-degenerate braided fusion categories
(European Mathematical Society, 2014-01)
We show that the Witt class of a weakly group-theoretical non-degenerate braided fusion category belongs to the subgroup generated by classes of non-degenerate pointed braided fusion categories and Ising braided categories. ...
Hochschild cohomology of algebras arising from categories and from bounded quivers
(European Mathematical Society, 2019-10)
The main objective of this paper is to provide a theory for computing the Hochschild cohomology of algebras arising from a linear category with finitely many objects and zero compositions. For this purpose, we consider ...
On exponential convergence of generic quantum Markov semigroups in a Wasserstein-type distance
(Publicaciones académicas Ltd., 2016)
We investigate about exponential convergence for generic quantum Markov semigroups using an generalization of the Lipschitz seminorm and a noncommutative analogue of Wasserstein distance. We show turns out to be closely ...
Topological Quantum Field Theories from Spherical Fusion Categories
(Universidad de los AndesMaestría en MatemáticasFacultad de CienciasDepartamento de Matemáticas, 2022-12-06)
The main topic of this work is the Turaev-Viro construction of a 3-dimensopnal topological quantum field theory (TQFT). We begin by giving a description of spherical fusion categories an it's associated graphical calculus. ...
Computational approaches for the sparse regression problem
(Universidad de los AndesMaestría en MatemáticasFacultad de CienciasDepartamento de Matemáticas, 2022)
This work introduces and describes three different formulations (and their respective algorithms) for the sparse regression problem and compare their performance under different models. Lastly, it presents an application ...