Type A Fusion Rules by Omar Saldarriaga

“…In this paper we will define fusion algebras and give the general construction to obtain them from affine lie algebras. We also give several known methods to compute the structure constants for fusion algebras of type A.…”
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Springer Fibers for the Minimal and the Minimal Special Nilpotent Orbits by Kim, Dongkwan

“…Abstract We describe Springer fibers corresponding to the minimal and minimal special nilpotent orbits of simple Lie algebras. As a result, we give an answer to the conjecture of Humphreys regarding some graphs attached to Springer fibers.…”
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INFINITESIMAL CHEREDNIK ALGEBRAS AS W-ALGEBRAS by Losev, I., Tsymbaliuk, Oleksandr

“…In this article we establish an isomorphism between universal infinitesimal Cherednik algebras and W-algebras for Lie algebras of the same type and 1-block nilpotent elements. …”
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On isomorphisms and invariants of finite dimensional complex filiform Leibniz algebras by Sattarovich, Rakhimov Isamiddin, Ural, Bekbaev

“…The method allows to classify all filiform Leibniz algebras (including filiform Lie algebras) in a given fixed dimensional case.…”
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Controlling several atoms in a cavity by Michael Keyl, Robert Zeier, Thomas Schulte-Herbrüggen

“…Hence we address problems arising with infinite-dimensional Lie algebras and those of unbounded operators. For the models considered, these problems can be solved by splitting the set of control Hamiltonians into two subsets: the first obeys an Abelian symmetry and can be treated in terms of infinite-dimensional Lie algebras and strongly closed subgroups of the unitary group of the system Hilbert space. …”
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Quiver theories and formulae for nilpotent orbits of Exceptional algebras by Amihay Hanany, Rudolph Kalveks

“…Abstract We treat the topic of the closures of the nilpotent orbits of the Lie algebras of Exceptional groups through their descriptions as moduli spaces, in terms of Hilbert series and the highest weight generating functions for their representation content. …”
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BPS states for scalar field theories based on g $$ \mathfrak{g} $$ 2 and su $$ \mathfrak{su} $$ (4) algebras by G. Luchini, T. Tassis

“…Abstract We discuss two models in 1 + 1 dimensional space-time for real scalar field multiplets on the root space of g $$ \mathfrak{g} $$ 2 and su $$ \mathfrak{su} $$ (4) Lie algebras. The construction of these models is presented and the corresponding BPS solutions are found.…”
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Verma modules for Iwasawa algebras are faithful by Ardakov, K, Wadsley, S

“…We also prove the algebraic independence of Arens-Michael envelopes over Iwasawa algebras and compute the centre of affinoid enveloping algebras of semisimple $p$-adic Lie algebras.…”

On the representations of disconnected reductive groups over F q by Lusztig, George

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Langlands duality for representations and quantum groups at a root of unity by McGerty, K

“…We give a representation-theoretic interpretation of the Langlands character duality of Frenkel and Hernandez, and show that the "Langlands branching multiplicities" for symmetrizable Kac-Moody Lie algebras are equal to certain tensor product multiplicities. …”

Geometric methods in physics : by Workshop on Geometrical Methods in Physics (27th : 2008 :, Kielanowski, P. (Piotr), 1944-

Seaweeds Arising from Brauer Configuration Algebras by Agustín Moreno Cañadas, Odette M. Mendez

“…It is worth noting that finding such an index for general Lie algebras is a cumbersome problem. On the other hand, Brauer configuration algebras are multiserial and symmetric algebras whose representation theory can be described using combinatorial data. …”
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Representations of rational Cherednik algebras by Rouquier, R

“…We insist on the analogy with the representation theory of complex semi-simple Lie algebras.…”

A binary encoding of spinors and applications by Arizmendi Gerardo, Herrera Rafael

“…As applications, we present explicit descriptions of the triality automorphism of Spin(8), explicit representations of the Lie algebras 𝔰𝔭𝔦𝔶 (8), 𝔰𝔭𝔦𝔶 (7) and 𝔤2, etc.…”
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Relations in Quantized Function Algebras by Etingof, Pavel I, Neshveyev, Sergey

“…In particular, we give presentations of quantized function algebras of automorphism groups of finite dimensional simple complex Lie algebras. Keyword: Quantized function algebras; C*-tensor categories; Quantum groups at roots of unity; Quasitriangular Hopf algebras…”
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On low-dimensional filiform leibniz algebras and their invariants. by Sattarovich, Rakhimov Isamiddin, Hassan, Munther A.

“…This subclass arises from the naturally graded filiform Lie algebras. We give a complete list of algebras. In parametric families cases, the corresponding orbit functions (invariants) are given. …”

LINEARIZATION OF POISSON–LIE STRUCTURES ON THE 2D EUCLIDEAN AND (1 + 1) POINCARÉ GROUPS by Bousselham Ganbouri, Mohamed Wadia Mansouri

“…For this, we calculate all Poisson-Lie structures on these two groups mentioned above, through the correspondence with Lie Bialgebra structures on their Lie algebras which we first determine.…”
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Quadripartitioned neutrosophic pythagorean lie subalgebra by R. Radha, A.Stanis Arul Mary

“…In this paper, we apply the notion of quadripartitioned Neutrosophic Pythagorean sets to Lie algebras. We develop the concept of QNP Lie subalgebras and QNP Lie ideals. …”
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The Sum of a Finite Group of Weights of a Hopf Algebra by Apoorva Khare

“…Examples include groups, (quantum groups over) Lie algebras, the small quantum groups of Lusztig, and their variations (by Andruskiewitsch and Schneider).…”
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Invertible Carnot Groups by Freeman David M.

“…We characterize Carnot groups admitting a 1-quasiconformal metric inversion as the Lie groups of Heisenberg type whose Lie algebras satisfy the J2-condition, thus characterizing a special case of inversion invariant bi-Lipschitz homogeneity. …”
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