Related papers: Poincare-Birkhoff-Witt Theorems
The so-called covariant Poincare lemma on the induced cohomology of the spacetime exterior derivative in the cohomology of the gauge part of the BRST differential is extended to cover the case of arbitrary, non reductive Lie algebras. As a…
We formulate analogues of the Birch and Swinnerton-Dyer conjecture for the $p$-adic $L$-functions of Bertolini-Darmon-Prasanna attached to elliptic curves $E/\mathbf{Q}$ at primes $p$ of good ordinary reduction. Using Iwasawa theory, we…
In this paper we present a generalization of the classical Hermite polynomials to the framework of Clifford-Dunkl operators. Several basic properties, such as orthogonality relations, recurrence formulae and associated differential…
We establish a universal approach to solution of the word problem in the varieties of di- and tri-algebras. This approach, for example, allows to apply Groebner---Shirshov bases method for Lie algebras to solve the ideal membership problem…
There is a relatively well understood class of deformable W-algebras, resulting from Drinfeld-Sokolov (DS) type reductions of Kac-Moody algebras, which are Poisson bracket algebras based on finitely, freely generated rings of differential…
In this sequel to arxiv:arXiv:1012.0835 we develop Bezout type theorems for semidegrees (including an explicit formula for {\em iterated semidegrees}) and an inequality for subdegrees. In addition we prove (in case of surfaces) a Bernstein…
This article deals with a number of topics which are, somewhat surprisingly, related. Firstly, the fundamental theorem of skew invariant theory for the symplectic group giving the generators and relations of symplectic invariants is…
This paper is the first in a series in which we offer a new framework for hermitian K-theory in the realm of stable $\infty$-categories. Our perspective yields solutions to a variety of classical problems involving Grothendieck-Witt groups…
The polysymplectic $(n+1)$-form is introduced as an analogue of the symplectic form for the De Donder-Weyl polymomentum Hamiltonian formulation of field theory. The corresponding Poisson brackets on differential forms are constructed. The…
We introduce a general theory of homological Milnor-Witt cycle modules over an excellent base scheme equipped with a dimension function, extending both Rost's cycle modules and Feld's theory over fields. To any such module we associate a…
This is an introductory document surveying several results in polynomial approximation, known as the Bramble-Hilbert lemma.
We review the construction and applications of exactly Poincar\'e invariant quantum mechanical models of few-degree of freedom systems. We discuss the construction of dynamical representations of the Poincar\'e group on few-particle Hilbert…
The purpose of this mostly expository paper is to discuss a connection between Nielsen fixed point theory and symplectic Floer homology theory for symplectomorphisms of surface and a calculation of Seidel's symplectic Floer homology for…
We consider free and proper cotangent-lifted symmetries of Hamiltonian systems. For the special case of G = SO(3), we construct symplectic slice coordinates around an arbitrary point. We thus obtain a parametrisation of the phase space…
We study a sequence of polynomials orthogonal with respect to a one parameter family of weights $$ w(x):=w(x,t)=\rex^{-t/x}\:x^{\al}(1-x)^{\bt},\quad t\geq 0, $$ defined for $x\in[0,1].$ If $t=0,$ this reduces to a shifted Jacobi weight.…
In arXiv:2011.06562, the first author and Otto van Koert proved a generalized version of the classical Poincar\'e-Birkhoff theorem, for Liouville domains of any dimension. In this article, we prove a relative version for Lagrangians with…
By means of fixed point index theory for multi-valued maps, we provide an analogue of the classical Birkhoff--Kellogg Theorem in the context of discontinuous operators acting on affine wedges in Banach spaces. Our theory is fairly general…
We develop the homological theory of KLR algebras of symmetric affine type. For each PBW basis, a family of standard modules is constructed which categorifies the PBW basis.
In this paper we present a right version of the algorithms developed for to compute Gr\"obner bases over bijective skew PBW extensions in the left case given in [3]. In particular, we adapt the theory of reduction and we build a right…
In this note, we use the concept of a polynomial ring to give an elementary proof to Cayley-Hamilton Theorem. We also give an elementary proof to Birkhoff theorem on Bi-stochastic matrices.