Related papers: Endofunctors and Poincar\'e-Birkhoff-Witt theorems
The braided approach to q-deformation (due to the author and collaborators) gives natural algebras $R_{21}u_1Ru_2=u_2R_{21}u_1R$ and $R_{21}x_1x_2=x_2x_1R$ for q-Minkowski and q-Euclidean spaces respectively. These algebras are covariant…
In this paper we study quantum group deformations of the infinite dimensional symmetry algebra of asymptotically AdS spacetimes in three dimensions. Building on previous results in the finite dimensional subalgebras we classify all possible…
We give an account of the basic combinatorial structure underlying the notion of type dependency. We do so by considering the category of all dependent sequent calculi, and exhibiting it as the category of algebras for a monad on a presheaf…
This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In two previous papers, we develop the basic theory of formal manifolds,…
We introduce the PBW degeneration for basic classical Lie superalgebras and construct for all type I, $\mathfrak{osp}(1,2n)$ and exceptional Lie superalgebras new monomial bases. These bases are parametrized by lattice points in convex…
We define Bernstein-Gelfand-Ponomarev reflection functors in the cluster categories of hereditary algebras. They are triangle equivalences which provide a natural quiver realization of the "truncated simple reflections" on the set of almost…
Let $Q$ be a finite type quiver i.e. ADE Dynkin quiver. Denote by $\Lambda$ its preprojective algebra. It is known that there are finitely many indecomposable $\Lambda$-modules if and only if $Q$ is of type $A_1,A_2,A_3,A_4$. In this paper,…
In this paper we generalize classical results on Lie algebras and universal enveloping algebras of Lie algebras to Lie-Rinehart algebras. We define for any Lie-Rinehart algebra $L$ and any cocycle $f$ in $Z^2(L,B)$, a universal enveloping…
Awodey, later with Newstead, showed how polynomial functors with extra structure (termed ``natural models'') hold within them the categorical semantics for dependent type theory. Their work presented these ideas clearly but ultimately led…
The present article takes advantage of the properties of algebras in the category of S-modules (twisted algebras) to investigate further the fine algebraic structure of Hopf operads. We prove that any Hopf operad P carries naturally the…
We construct a universal envelope for any Poisson- and Gerstenhaber algebra. While the deformation theory of Poisson algebras seems to be partially trivial, results from string- and M-theory suggest a rich deformation theory of Gerstenhaber…
We develop the necessary tools, including a notion of logarithmic derivative for curves in homogeneous spaces, for deriving a general class of equations including Euler-Poincar\'e equations on Lie groups and homogeneous spaces. Orbit…
The global qualitative behaviour of fields of principal directions for the graph of a real valued polynomial function $f$ on the plane are studied. We provide a Poincar\'e-Hopf type formula where the sum over all indices of the principal…
A class of Z_2-graded Lie algebra and Lie superalgebra extensions of the pseudo-orthogonal algebra of a spacetime of arbitrary dimension and signature is investigated. They have the form g = g_0 + g_1, with g_0 = so(V) + W_0 and g_1 = W_1,…
In this paper we consider the structure of general quantum W-algebras. We introduce the notions of deformability, positive-definiteness, and reductivity of a W-algebra. We show that one can associate a reductive finite Lie algebra to each…
We present a higher-dimensional version of the Poincar\'e-Birkhoff theorem which applies to Poincar\'e time maps of Hamiltonian systems. The maps under consideration are neither required to be close to the identity nor to have a monotone…
Garret Birkhoff's HSP theorem characterizes the classes of models of algebraic theories as those being closed with respect to homomorphic images, subalgebras, and products. In particular, it implies that an algebra $\mathbf{B}$ satisfies…
Taking inspiration from the monadicity of complete atomic Boolean algebras, we prove that profinite modal algebras are monadic over Set. While analyzing the monadic functor, we recover the universal model construction - a construction…
We consider the finite $W$-algebra $U(\g,e)$ associated to a nilpotent element $e \in \g$ in a simple complex Lie algebra $\g$ of exceptional type. Using presentations obtained through an algorithm based on the PBW-theorem, we verify a…
In 2008, Loday shed light on the existence of Hopf-Boreltheorems for operads. Using the vocabulary of category theory, Livernet,Mesablishvili and Wisbauer extended such theorems to monads. In bothcases, the reasoning was to start from a…