Algebraic (super-)integrability from commutants of subalgebras in universal enveloping algebras [PDF]
Journal of Physics A: Mathematical and Theoretical, 2023 Abstract Starting from a purely algebraic procedure based on the commutant of a subalgebra in the universal enveloping algebra of a given Lie algebra, the notion of algebraic Hamiltonians and the constants of the motion generating a polynomial symmetry algebra is proposed. The case of the special linear Lie algebra
Rutwig Campoamor-Stursberg +3 more
semanticscholar +7 more sources
Algebras, traces, and boundary correlators in N $$ \mathcal{N} $$ = 4 SYM [PDF]
Journal of High Energy Physics, 2021 We study supersymmetric sectors at half-BPS boundaries and interfaces in the 4d N $$ \mathcal{N} $$ = 4 super Yang-Mills with the gauge group G, which are described by associative algebras equipped with twisted traces.
Mykola Dedushenko, Davide Gaiotto
doaj +2 more sources
$ \mathbb{Z}_2 \times \mathbb{Z}_2 $ generalizations of ${\cal N} = 1$ superconformal Galilei algebras and their representations [PDF]
Journal of Mathematics and Physics, 2018 We introduce two classes of novel color superalgebras of $ \mathbb{Z}_2 \times \mathbb{Z}_2 $ grading. This is done by realizing members of each in the universal enveloping algebra of the ${\cal N}=1$ supersymmetric extension of the conformal Galilei ...
Aizawa, N., Isaac, P. S., Segar, J.
core +2 more sources
Duals of coloured quantum universal enveloping algebras and coloured universal $\cal T$-matrices [PDF]
, 1997 We extend the notion of dually conjugate Hopf (super)algebras to the coloured Hopf (super)algebras ${\cal H}^c$ that we recently introduced. We show that if the standard Hopf (super)algebras ${\cal H}_q$ that are the building blocks of ${\cal H}^c$ have ...
C. Quesne, Chakrabarti R.
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Hopf algebras for ternary algebras [PDF]
, 2009 We construct an universal enveloping algebra associated to the ternary extension of Lie (super)algebras called Lie algebra of order three. A Poincar\'e-Birkhoff-Witt theorem is proven is this context.
de Traubenberg, M. Rausch, Goze, M.
core +4 more sources
BRST operator for quantum Lie algebras and differential calculus on quantum groups
, 2001 For a Hopf algebra A, we define the structures of differential complexes on two dual exterior Hopf algebras: 1) an exterior extension of A and 2) an exterior extension of the dual algebra A^*.
Isaev, A. P., Ogievetsky, O. V.
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The structure group for quasi-linear equations via universal enveloping algebras [PDF]
Communications of the American Mathematical Society, 2021 We replace trees by multi-indices as an index set of the abstract model space to tackle quasi-linear singular stochastic partial differential equations.
P. Linares, F. Otto, Markus Tempelmayr
semanticscholar +1 more source
Universal Enveloping Algebras of Poisson Superalgebras [PDF]
Algebras and Representation Theory, 2021 In this paper, we define and study the universal enveloping algebra of a Poisson superalgebra. In particular, a new PBW Theorem for Lie-Rinehart superalgebras is proved leading to a PBW Theorem for Poisson superalgebras, we show the universal enveloping ...
T. Lamkin
semanticscholar +1 more source
On Lie algebras in braided categories [PDF]
, 1996 The set of primitive elements of a Hopf algebra in the braided category of group graded vector spaces (with a commutative group) carry the structure of a generalized Lie algebra.
B. Pareigis
semanticscholar +1 more source
Gradings, Braidings, Representations, Paraparticles: Some Open Problems
Axioms, 2012 A research proposal on the algebraic structure, the representations and the possible applications of paraparticle algebras is structured in three modules: The first part stems from an attempt to classify the inequivalent gradings and braided group ...
Konstantinos Kanakoglou
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