Results 1 to 10 of about 3,464 (73)
Algebraic (super-)integrability from commutants of subalgebras in universal enveloping algebras
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
openaire +6 more sources
Universal Enveloping Algebras of Lie Antialgebras
Algebras and Representation Theory, 2010 Lie antialgebras is a class of supercommutative algebras recently appeared in symplectic geometry. We define the notion of enveloping algebra of a Lie antialgebra and study its properties.
Leidwanger, Séverine +1 more
core +3 more sources
Algebras, traces, and boundary correlators in N $$ \mathcal{N} $$ = 4 SYM
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 +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
doaj +1 more source
Indecomposable finite-dimensional representations of a class of Lie algebras and Lie superalgebras [PDF]
, 2011 In the article at hand, we sketch how, by utilizing nilpotency to its fullest extent (Engel, Super Engel) while using methods from the theory of universal enveloping algebras, a complete description of the indecomposable representations may be reached ...
G Cassinelli +5 more
core +1 more source
Hopf algebras for ternary algebras
, 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 +3 more sources
Hopf Structure and Green Ansatz of Deformed Parastatistics Algebras [PDF]
, 2005 Deformed parabose and parafermi algebras are revised and endowed with Hopf structure in a natural way. The noncocommutative coproduct allows for construction of parastatistics Fock-like representations, built out of the simplest deformed bose and ...
Boyka Aneva +12 more
core +2 more sources
Duals of coloured quantum universal enveloping algebras and coloured universal $\cal T$-matrices
, 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.
core +1 more source
, 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.
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Representation theory of super Yang-Mills algebras [PDF]
, 2011 We study in this article the representation theory of a family of super algebras, called the \emph{super Yang-Mills algebras}, by exploiting the Kirillov orbit method \textit{\`a la Dixmier} for nilpotent super Lie algebras.
A. Connes +22 more
core +2 more sources