Related papers: Non-commutative divergence and the Turaev cobracke…
In this contributed presentation, we discuss and compare the mutually opposite procedures of deformations and contractions of Lie algebras. We suggest that with appropriate combinations of both procedures one may construct new Lie algebras.…
We establish a bijective correspondence between isomorphism classes of basic silting objects of $\mathsf{per}(A)$ and algebraic $t$-structures of $\mathsf{D}_{\rm fd}(A)$ for locally finite non-positive dg algebra $A$ over a field $k$ (more…
We study Poisson symmetric spaces of group type with Cartan subalgebra "adapted" to the Lie cobracket.
This is an extended version of a communication made at the international conference ``Noncommutative Geometry and Physics'' held at Orsay in april 2007. In this proceeding, we make a review of some noncommutative constructions connected to…
We study the Hamilton formalism for Connes-Lott models, i.e., for Yang-Mills theory in non-commutative geometry. The starting point is an associative $*$-algebra $\cA$ which is of the form $\cA=C(I,\cAs)$ where $\cAs$ is itself a…
We study lattices in non-positively curved metric spaces. Borel density is established in that setting as well as a form of Mostow rigidity. A converse to the flat torus theorem is provided. Geometric arithmeticity results are obtained…
We survey some aspects of the theory of noncommutative manifolds focusing on the noncommutative analogs of two-dimensional tori and low-dimensional spheres. We are particularly interested in those aspects of the theory that link the…
We derive formulas for the Reshetikhin-Turaev invariants of all oriented Seifert manifolds associated to an arbitrary complex finite dimensional simple Lie algebra $\mathfrak g$ in terms of the Seifert invariants and standard data for…
Some equivalence classes in symmetric group lead to an interesting class of noncommutive and associative algebras. From these algebras we construct noncommutative Frobenius algebras. Based on the correspondence between Frobenius algebras…
A novel algorithm is provided to couple a Galilean invariant model with curved spatial background by taking nonrelativistic limit of a unique minimally coupled relativistic theory, which ensures Galilean symmetry in the flat limit and…
We present an algorithm for the computation of the topological type of a real compact Riemann surface associated to an algebraic curve, i.e., its genus and the properties of the set of fixed points of the anti-holomorphic involution $\tau$,…
We consider Open Gromov-Witten invariants for noncompact Calabi-Yau in the case the Lagrangian has the topology of $\R^2 \times S^1$. The definition of the invariant involves the choice of a frame for the Lagrangian, in accord with string…
In this article, we define a non-commutative deformation of the "symplectic invariants" of an algebraic hyperelliptical plane curve. The necessary condition for our definition to make sense is a Bethe ansatz. The commutative limit reduces…
Quasi-Lie bialgebras are natural extensions of Lie-bialgebras, where the cobracket satisfies the co-Jacobi relation up to some natural obstruction controlled by a skew-symmetric 3-tensor $\phi$. This structure was introduced by Drinfeld…
We expand on some invariants used for classifying nonselfadjoint operator algebras. Specifically to nonselfadjoint operator algebras which have a conditional expectation onto a commutative diagonal we construct an edge-colored directed…
We study the dynamics of a symplectic twist map without conjugate points. We show that in a neighborhood of a totally periodic Lagrangian manifold, there exists a large family of invariant Lagrangian tori on which the twist map is…
Let $G/\Gamma$ be the quotient of a semisimple Lie group by an arithmetic lattice. We show that for reductive subgroups $H$ of $G$ that is large enough, the orbits of $H$ on $G/\Gamma$ intersect nontrivially with a fixed compact set. As a…
We study free dg-Lie algebroids over arbitrary derived schemes, and compute their universal enveloping and jet algebras. We also introduce derived twisted connections, and relate them with lifts on twisted square zero extensions. This…
We prove a noncommutative variant of Saskin's classical theorem -- on the connection between Choquet boundaries for function spaces and Korovkin sets -- for operator systems generating separable Type I C*-algebras. The main result implies…
We prove that the mirror map is the SYZ map for every toric Calabi-Yau surface. As a consequence one obtains an enumerative meaning of the mirror map. This involves computing genus-zero open Gromov-Witten invariants, which is done by…