相关论文: Yangian of the periplectic Lie superalgebra
We study the (extended) orthogonal Yangians associated to the Lie algebras types $B$ and $D$ over a field of positive characteristic. We define the $p$-center for the Yangians and obtain an explicit description of the center in terms of…
We show explicitly a generalised Lie algebra embedded in the positive and negative parts of the Drinfeld-Jimbo quantum groups of type A_n. Such a generalised Lie algebra satisfy axioms closely related to the ones found by S.L. Woronowicz.…
For every family of orthogonal polynomials, we define a new realization of the Yangian of ${\mathfrak{gl}}_n$. Except in the case of Dickson polynomials, the new realizations do not satisfy the RTT relation. We obtain an analogue of the…
We study a class of quantized enveloping algebras, called twisted Yangians, associated with the symmetric pairs of types B, C, D in Cartan's classification. These algebras can be regarded as coideal subalgebras of the extended Yangian for…
We prove a version of the Poincar\'e-Birkhoff-Witt Theorem for profinite pronilpotent Lie algebras in which their symmetric and universal enveloping algebras are replaced with appropriate formal analogues and discuss some immediate…
We study the structure of quantized enveloping algebras called twisted Yangians, which are naturally associated with the B, C, and D series of the classical Lie algebras. We obtain an explicit formula for the formal series (the Sklyanin…
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…
It is shown that the quantised enveloping algebra of sl(n) contains a quantum Lie algebra, defined by means of axioms similar to Woronowicz's., This gives rise to Lie algebra-like generators and relations for the locally finite part of the…
We study the family of Bethe subalgebras in the Yangian $Y(\mathfrak{g})$ parameterized by the corresponding adjoint Lie group $G$. We describe their classical limits as subalgebras in the algebra of polynomial functions on the formal Lie…
We give a detailed derivation of the commutation relations for the Poincar\'e--Birkhoff--Witt generators of the quantum superalgebra $\mathrm U_q(\mathfrak{gl}_{M|N})$.
We use the Gauss decomposition of the generator matrix in the $R$-matrix presentation of the Yangian for the orthosymplectic Lie superalgebra ${\frak osp}_{N|2m}$ to produce its Drinfeld-type presentation. The results rely on a…
We prove denominator identities for the periplectic Lie superalgebra $\mathfrak{p}(n)$, thereby completing the problem of finding denominator identities for all simple classical finite-dimensional Lie superalgebras.
The twisted q-Yangians are coideal subalgebras of the quantum affine algebra associated with gl(N). We prove a classification theorem for finite-dimensional irreducible representations of the twisted q-Yangians associated with the…
Let $d$ be a positive integer. The Yangian $Y_d=Y(\mathfrak{gl}(d,\mathbb C))$ of the general linear Lie algebra $\mathfrak{gl}(d,\mathbb C)$ has countably many generators and quadratic-linear defining relations, which can be packed into a…
A methodical analysis of the research related to the article, ``Sur les groupes continus'', of Henri Poincar\'{e} reveals many historical misconceptions and inaccuracies regarding his contribution to Lie theory. A thorough reading of this…
We introduce the notion of Poisson superbialgebra as an analogue of Drinfeld's Lie superbialgebras. We extend various known constructions dealing with representations on Lie superbialgebras to Poisson superbialgebras. We introduce the…
We derive some new presentations for the Yangian associated to the Lie algebra gl_n(C) that are adapted to parabolic subalgebras. At one extreme, the presentation is just the usual RTT presentation, whilst at the other extreme it is a…
We classify the finite-dimensional irreducible representations of the super Yangian associated with the orthosymplectic Lie superalgebra ${\frak osp}_{2|2n}$. The classification is given in terms of the highest weights and Drinfeld…
We study the Yangian $Y_n$ associated to the general linear Lie algebra $\mathfrak{gl}_n$ over a field of positive characteristic, as well as its shifted analog $Y_n(\sigma)$. Our main result gives a description of the centre of…
A proof of Poincar\'e-Birkhoff-Witt theorem is given for a class of generalized Lie algebras closely related to the Gurevich S-Lie algebras. As concrete examples, we construct the positive (negative) parts of the quantized universal…