Related papers: (3+1)-Dimensional Schwinger Terms and Non-commutat…
We establish results about the second cohomology with coefficients in the trivial module, symmetric invariant bilinear forms and derivations of a Lie algebra extended over a commutative associative algebra without unit. These results…
Using new configuration spaces, we give an explicit construction that extends Kontsevich's Lie-infinity quasi-isomorphism from polyvector fields to Hochschild cochains to a quasi-isomorphism of A-infinity algebras equipped with actions by…
We write down scalar field theory and gauge theory on two-dimensional noncommutative spaces ${\cal M}$ with nonvanishing curvature and non-constant non-commutativity. Usual dynamics results upon taking the limit of ${\cal M}$ going to i) a…
In this review article, first we give the concrete formulas of representations and cohomologies of associative algebras, Lie algebras, pre-Lie algebras, Leibniz algebras and 3-Lie algebras and some of their strong homotopy analogues. Then…
In this paper a general van Est type isomorphism is established. The isomorphism is between the Lie algebra cohomology of a bicrossed sum Lie algebra and the Hopf cyclic cohomology of its Hopf algebra. We first prove a one to one…
We study the L-infinity-formality problem for the Hochschild complex of the universal enveloping algebra of some examples of Lie algebras such as Cartan-3-regular quadratic Lie algebras (for example semisimple Lie algebras and in more…
We give a new computation of Hochschild (co)homology of the exterior algebra, together with algebraic structures, by direct comparison with the symmetric algebra. The Hochschild cohomology is determined to be essentially the algebra of…
We construct a seven-term exact sequence involving low degree cohomology spaces of a Lie algebra $\Lg$, an ideal $\Lh$ of $\Lg$ and the quotient $\Lg / \Lh$ with coefficients in a $\Lg$-module. The existence of such a sequence follows from…
Let $p$ and $q$ be distinct prime numbers. We study the Galois objects and cocycle deformations of the noncommutative, noncocommutative, semisimple Hopf algebras of odd dimension $p^3$ and of dimension $pq^2$. We obtain that the $p+1$…
We introduce a class of densely defined, unbounded, 2-Hochschild cocycles ([PT]) on finite von Neumann algebras $M$. Our cocycles admit a coboundary, determined by an unbounded operator on the standard Hilbert space associated to the von…
We develop the cohomology theory of color Lie superalgebras due to Scheunert--Zhang in a framework of nonhomogeneous quadratic Koszul algebras. In this approach, the Chevalley--Eilenberg complex of a color Lie algebra becomes a standard…
The Einstein-Hilbert action in three dimensions and the transformation rules for the dreibein and spin connection can be naturally described in terms of gauge theory. In this spirit, we use covariant coordinates in noncommutative gauge…
We study geodesics in noncommutative geometry by means of bimodule connections and completely positive maps using the Kasparov, Stinespring, Gel'fand, Naimark & Segal (KSGNS) construction. This is motivated from classical geometry, and we…
The commutator anomalies (Schwinger terms) of current algebras in $3+1$ dimensions are computed in terms of the Wodzicki residue of pseudodifferential operators; the result can be written as a (twisted) Radul 2-cocycle for the Lie algebra…
We propose a generalization of non-commutative geometry and gauge theories based on ternary Z_3-graded structures. In the new algebraic structures we define, we leave all products of two entities free, imposing relations on ternary products…
In the first part we present the Weyl algebra and our results concerning its finite-dimensional Lie subalgebras. The second part is devoted to a more exotic algebraic structure, the Lie algebra of order 3. We set the basis of a theory of…
We introduce a covariant non-commutative deformation of 3+1-dimensional conformal field theory. The deformation depends on a short-distance scale \ell_p, and thus breaks scale invariance, but preserves all space-time isometries. The…
The free Schr\"odinger equation with mass M can be turned into a non-massive Klein-Gordon equation via Fourier transformation with respect to M. The kinematic symmetry algebra sch_d of the free d-dimensional Schr\"odinger equation with M…
The approach for Poisson bialgebras characterized by Manin triples with respect to the invariant bilinear forms on both the commutative associative algebras and the Lie algebras is not available for giving a bialgebra theory for transposed…
After introducing a noncommutative counterpart of commutative algebraic geometry based on monoidal categories of quasi-coherent sheaves we show that various constructions in noncommutative geometry (e.g. Morita equivalences, Hopf-Galois…