Related papers: Equivariant Cartan Homotopy Formulae for $DG$-Alge…

Using the formalism of discrete quantum group gauge theory, one can construct the quantum algebras of observables for the Hamiltonian Chern-Simons model. The resulting moduli algebras provide quantizations of the algebra of functions on the…

In this paper we compute homotopical bordism rings $MU^G_*$ for abelian compact Lie groups G, giving explicit generators and relations. The key constructions are operations on equivariant bordism which should play an important role in…

Any finite-dimensional commutative (associative) graded algebra with all nonzero homogeneous subspaces one-dimensional is defined by a symmetric coefficient matrix. This algebraic structure gives a basic kind of $A$-graded algebras…

Quantum Chern-Simons invariants of differentiable manifolds are analyzed from the point of view of homological algebra. Given a manifold M and a Lie (or, more generally, an L-infinity) algebra g, the vector space H^*(M) \otimes g has the…

We describe a general method for algorithmic construction of G-equivariant chain homotopy equivalences from non-equivariant ones. As a consequence, we obtain an algorithm for computing equivariant (co)homology of Eilenberg-MacLane spaces…

We show that the invariants of a free associative algebra of finite rank under a linear action of a finite-dimensional Hopf algebra generated by group-like and skew-primitive elements form a finitely generated algebra exactly when the…

We develop a theory of equivariant factorization algebras on varieties with an action of a connected algebraic group $G$, extending the definitions of Francis-Gaitsgory [FG] and Beilinson-Drinfeld [BD1] to the equivariant setting. We define…

We implement the Hamiltonian treatment of a nonAbelian noncommutative gauge theory, considering with some detail the algebraic structure of the noncommutative symmetry group. The first class constraints and Hamiltonian are obtained and…

We introduce the notion of a graded group action on a graded algebra or, which is the same, a group action by graded pseudoautomorphisms. An algebra with such an action is a natural generalization of an algebra with a super- or a…

Let G be a finite group. We study the group of G-equivariant self-homotopy equivalences of product of G-spaces. For a product of n-spaces, we represent it as product of n-subgroups under the assumption of equivariant reducibility. Further…

Let g be a Lie bialgebra and let V be a finite-dimensional g-module. We study deformations of the symmetric algebra of V which are equivariant with respect to an action of the quantized enveloping algebra of g. In particular we investigate…

Equivariant Riemann-Roch theorem for the complex variety under the action of complex linear reductive algebraic group.

The algebraic formulation of the quantum group covariant noncommutative geometry in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider structure groups taking values in the quantum groups and…

We discuss in this paper the conformal geometry of bi-invariant metrics on compact semisimple Lie groups. For this purpose we develop a conformal Cartan calculus adapted to this problem. In particular, we derive an explicit formula for the…

We compute equivariant fundamental classes of orbits in GL(2)-representations. As applications, we find degrees of the orbit closures corresponding to elliptic fibrations and self-maps of the projective line.

Let $\mathcal{J}$ be the exceptional Jordan algebra and $V=\mathcal{J}\oplus \mathcal{J}$. We construct an equivariant map from $V$ to $\mathrm{Hom}_k(\mathcal{J}\otimes \mathcal{J},\mathcal{J})$ defined by homogeneous polynomials of degree…

We investigate the combinatorial data arising from the classification of equivariant homotopy commutativity for cyclic groups of order $G=C_{p_1 \cdots p_n}$ for $p_i$ distinct primes. In particular, we will prove a structural result which…

The familiar Fourier-Mukai technique can be extended to an equivariant setting where a finite group $G$ acts on a smooth projective variety $X$. In this paper we compare the group of invariant autoequivalences $\Aut(D(X))^G$ with the group…

In this paper, we prove an equivariant version of the classical Dold-Thom theorem. Associated to a finite group, a CW-complex on which this group acts and a covariant coefficient system in the sense of Bredon, we functorially construct a…

We set up an algebraic framework for the study of pseudoholomorphic discs bounding nonorientable Lagrangians, as well as equivariant extensions of such structures arising from a torus action. First, we define unital cyclic twisted…