相关论文: Poincar\'e--Birkhoff--Witt isomorphisms and Kapran…

Let $U$ be a connected, simply connected compact Lie group with complexification $G$. Let $\mathfrak{u}$ and $\mathfrak{g}$ be the associated Lie algebras. Let $\Gamma$ be the Dynkin diagram of $\mathfrak{g}$ with underlying set $I$, and…

On a prequantizable K\"ahler manifold $(M, \omega, L)$, Chan-Leung-Li constructed a genuine (non-asymptotic) action of a subalgebra of the Berezin-Toeplitz star product on $H^0(M, L^{\otimes k})$ for each level $k$ [14]. We extend their…

We establish a degeneration isomorphism between quantum toroidal algebras and untwisted affine Yangians, valid for all untwisted affine Kac-Moody Lie algebras. Specifically, we prove that the affine Yangian $Y_\hbar(\mathfrak{g})$ is…

For a Lie algebroid pair $A\hookrightarrow L$ we study cocycles constructed from the extension to $L$ of the higher connection forms of a representation up to homotopy $E$ of the Lie algebroid $A$. We show that there exists a cohomology…

We study the Lie bialgebra structures that can be built on the one-dimensional central extension of the Poincar\'e and (A)dS algebras in (1+1) dimensions. These central extensions admit more than one interpretation, but the simplest one is…

Inspired by the recent work of Chen-Sti\'enon-Xu on Atiyah classes associated to inclusions of Lie algebroids, we give a very simple criterium (in terms of those classes) for relative Poincar\'e-Birkhoff-Witt type results to hold. The tools…

A well-known and old result of Hazewinkel and Koszul states that the cohomology of a finite-dimensional Lie algebra is isomorphic, up to a suitable shift, to its twisted homology, a Lie-theoretical version of Poincare duality. This paper…

For an $n$-dimensional Leibniz/Lie algebra $\mathfrak{h}$ over a field $k$ we introduce a new invariant ${\mathcal A}(\mathfrak{h})$, called the \emph{universal algebra} of $\mathfrak{h}$, as a quotient of the polynomial algebra $k[X_{ij}…

A procedure to determine the initial ansatz for the co-frame and spin connection characterizing a Riemann-Cartan geometry respecting a given group of continuous symmetries is illustrated. Given a particular group of symmetries and assuming…

We show that every Lie algebra or superLie algebra has a canonical braiding on it, and that in terms of this its enveloping algebra appears as a flat space with braided-commuting coordinate functions. This also gives a new point of view…

We introduce a canonical Chern-Weil map for possibly non-commutative g-differential algebras with connection. Our main observation is that the generalized Chern-Weil map is an algebra homomorphism ``up to g-homotopy''. Hence, the induced…

Leavitt path algebras L of an arbitrary graph E over a field K satisfying a polynomial identity are completely characterized both in graph-theoretic and algebraic terms. When E is a finite graph, L satisfying a polynomial identity is shown…

Let $G$ be a simply connected Lie group with Lie algebra $\mathfrak{g}$ and denote by $\mathrm{C}_{\bullet}(G)$ the DG Hopf algebra of smooth singular chains on $G$. In a companion paper it was shown that the category of sufficiently smooth…

We prove an algebraic version of the Gauge-Invariant Uniqueness Theorem, a result which gives information about the injectivity of certain homomorphisms between ${\mathbb Z}$-graded algebras. As our main application of this theorem, we…

We study the deformation complex of a canonical morphism $i$ from the properad of (degree shifted) Lie bialgebras $\mathbf{Lieb}_{c,d}$ to its polydifferential version $\mathcal{D}(\mathbf{Lieb}_{c,d})$ and show that it is quasi-isomorphic…

We introduce the notions of Atiyah class and Todd class of a differential graded vector bundle with respect to a differential graded Lie algebroid. We prove that the space of vector fields on a dg-manifold with homological vector field $Q$…

Let G be a Lie group with Lie algebra $ \Cal G: = T_\epsilon G$ and $T^*G = \Cal G^* \rtimes G$ its cotangent bundle considered as a Lie group, where G acts on $\Cal G^*$ via the coadjoint action. We show that there is a 1-1 correspondance…

We settle several questions about the theory of universal deformation quantization of Lie bialgebras by giving their complete classification up to homotopy equivalence. An important new technical ingredient introduced in this paper is an…

For a $\Gamma$--equivariant holomorphic Lie algebroid $(V,\, \phi)$, on a compact Riemann surface $X$ equipped with an action of a finite group $\Gamma$, we investigate the equivariant holomorphic Lie algebroid connections on holomorphic…

Let $K$ be any field, let $L_n$ denote the Leavitt algebra of type $(1,n-1)$ having coefficients in $K$, and let ${\rm M}_d(L_n)$ denote the ring of $d \times d$ matrices over $L_n$. In our main result, we show that ${\rm M}_d(L_n) \cong…