Related papers: Link Invariants, Holonomy Algebras and Functional …

The pro-algebraic fundamental group can be understood as a completion with respect to finite-dimensional non-commutative algebras. We introduce finer invariants by looking at completions with respect to Banach and C*-algebras, from which we…

Let L->M be a Hermitian line bundle over a compact manifold. Write S for the space of all unitary connections in L whose curvatures define symplectic forms on M and G for the group of unitary bundle isometries of L, which acts on S by…

A function that is analytic on a domain of $\mathbb{C}^n$ is holonomic if it is the solution to a holonomic system of linear homogeneous differential equations with polynomial coefficients. We define and study the Bernstein-Sato polynomial…

Let ${\sf G}$ be a locally compact group, $\mathscr C\overset{q}{\to}{\sf G}$ a Fell bundle and $\mathfrak B=L^1({\sf G}\,\vert\,\mathscr C)$ the algebra of integrable cross-sections associated to the bundle. We give conditions that…

We present a definition of an invariant #(M,H), defined for every finite-dimensional Hopf algebra (or Hopf superalgebra or Hopf object) H and for every closed, framed 3-manifold M. When H is a quantized universal enveloping algebra, #(M,H)…

Let P be a principal bundle with semisimple compact simply connected structure group G over a compact simply connected four-manifold M. In this note we give explicit formulas for the rational homotopy groups and cohomology algebra of the…

In 2014, Voronov introduced the notion of thick morphisms of (super)manifolds as a tool for constructing $L_{\infty}$-morphisms of homotopy Poisson algebras. Thick morphisms generalise ordinary smooth maps, but are not maps themselves.…

Let $S$ be the affine plane $\C^2$ together with an appropriate $\mathbb T = \C^*$ action. Let $\hil{m,m+1}$ be the incidence Hilbert scheme. Parallel to \cite{LQ}, we construct an infinite dimensional Lie algebra that acts on the direct…

We define a monad M on a category of measurable bornological sets, and we show how this monad gives rise to a theory of vector-valued integration that is related to the notion of Pettis integral. We show that an algebra X of this monad is a…

A kind of generalized Gelfand pair is introduced via a Banach algebra consisting of bi-invariant functions in a weighted Lebesgue space. The related spherical functions and the Fourier transformation are constructed. The multipliers of the…

We study homomorphisms on the algebra of analytic functions of bounded type on a Banach space. When the domain space lacks symmetric regularity, we show that in every fiber of the spectrum there are evaluations (in higher duals) which do…

We study the geometry and the singularities of the principal direction of the Drinfeld-Lafforgue-Vinberg degeneration of the moduli space of G-bundles Bun_G for an arbitrary reductive group G, and their relationship to the Langlands dual…

Presented is a structure theorem for the Leibniz Homology, HL_*, of an Abelian extension of a simple real Lie algebra g. As applications, results are stated for affine extensions of the classical Lie algebras sl_n(R), so_n(R), and sp_n(R).…

Suppose that $B$ is a $G$-Banach algebra over $\mathbb{F} = \mathbb{R}$ or $\mathbb{C}$, $X$ is a finite dimensional compact metric space, $\zeta : P \to X$ is a standard principal $G$-bundle, and $A_\zeta = \Gamma (X, P \times_G B)$ is the…

A detailed study of the semigroup $C^\ast$-algebra is presented. This $C^\ast$-algebra appears as a "deformation" of the continuous functions algebra on a compact abelian group. Considering semigroup $C^\ast$-algebras in this framework we…

Let G be a locally compact group, M(G) denote its measure algebra and L^1(G) denote its group algebra. Also, let pi:G->U(H) be a strongly continuous unitary representation, and let CB^{sigma}(B(H)) be the space of normal completely bounded…

Let $G$ be a discrete group, let $p\ge1$, and let $\omega$ be a weight on $G$. Using the approach from [9], we provide sufficient conditions on a weight $\omega$ for $\ell^p(G,\omega)$ to be a Banach algebra admitting a norm-controlled…

The space of de Rham currents supported in finitely many points in a Lie group $G$ has the structure of a filtered differential graded Hopf algebra. The product is given by convolution of compactly supported currents, and the co-product…

The quantum analogue of general relativistic geometry should be implementable on smooth manifolds without an a priori metric structure, the kinematical covariance group acting by diffeomorphisms. Here I approach quantum gravity (QG) in the…

This work investigates analytic Hilbert modules $\mathcal{H}$, over the polynomial ring, consisting of holomorphic functions on a $G$-space $\Omega \subset \mathbb{C}^m$ that are homogeneous under the natural action of the group $G$. In a…