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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 ...
The cohomology of monogenic extensions in the noncommutative setting
(Academic Press Inc Elsevier Science, 2008-06)
We extend the notion of monogenic extension to the noncommutative setting, and we study the Hochschild cohomology ring of such an extension. As an application we complete the computation of the cohomology ring of the rank ...
Correlation functions in the non-commutative Wess-Zumino-Witten model
(Elsevier Science, 2001-06)
We develop a systematic perturbative expansion and compute the one-loop two-points, three-points and four-points correlation functions in a non-commutative version of the U (N) Wess-Zumino-Witten model in different regimes ...
Isomorphisms of Nonnoetherian Down-Up Algebras
(Springer, 2018-12)
We solve the isomorphism problem for nonnoetherian down-up algebras A(α, 0, γ) by lifting isomorphisms between some of their noncommutative quotients. The quotients we consider are either quantum polynomial algebras in two ...
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, ...
Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration
(Elsevier Inc, 2012-12)
In the present paper, we are interested in natural quantum analogues of Richardson varieties in the type A grassmannians. To be more precise, the objects that we investigate are quantum analogues of the homogeneous coordinate ...
Homogeneous manifolds from noncommutative measure spaces
(Academic Press Inc Elsevier Science, 2010-05)
Let M be a finite von Neumann algebra with a faithful trace τ. In this paper we study metric geometry of homogeneous spaces O of the unitary group U of M, endowed with a Finsler quotient metric induced by the p-norms of ...
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 ...
Dynamics of algebras in quantum unstable systems
(World Scientific, 2018-07)
We introduce a dynamical evolution operator for dealing with unstable physical process, such as scattering resonances, photon emission, decoherence and particle decay. With that aim, we use the formalism of rigged Hilbert ...
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 ...