Nested Polyhedra and Indices of Orbits of Coxeter Groups of Non-Crystallographic Type by Mariia Myronova, Jiří Patera, Marzena Szajewska

“…The invariants of finite-dimensional representations of simple Lie algebras, such as even-degree indices and anomaly numbers, are considered in the context of the non-crystallographic finite reflection groups <inline-formula><math display="inline"><semantics><msub><mi>H</mi><mn>2</mn></msub></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><msub><mi>H</mi><mn>3</mn></msub></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><msub><mi>H</mi><mn>4</mn></msub></semantics></math></inline-formula>. …”
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The geometrical language of continuum mechanics / by Epstein, M. (Marcelo)

Quiver subtractions by Santiago Cabrera, Amihay Hanany

“…One is the extension of the physical realization of Kraft-Procesi transitions from the classical to the exceptional Lie algebras. Another result is the extension from special nilpotent orbits to non-special ones. …”
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Surjectivity of certain adjoint operators and applications by Amina Cherifi Hadjiat, Azzeddine Lansari

“…Indeed, these authors, in their work about the finite co-dimension ideals of Lie algebras of vector fields, restricted their study to fields $$X_0$$ X 0 of the form $$X_0=\sum _{i=1}^{n}( \alpha _i \cdot x_i+\beta _i\cdot x_i^{1+m_i}) \frac{\partial }{\partial x_i}$$ X 0 = ∑ i = 1 n ( α i · x i + β i · x i 1 + m i ) ∂ ∂ x i , where $$\alpha _i, \beta _i $$ α i , β i are positive and $$m_i$$ m i are even natural integers. …”
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On algebraic singularities, finite graphs and D-brane gauge theories : a string theoretic perspective -- with a digression on string field theory by He, Yang-Hui, 1975-

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The affine Yangian of gl₁, and the infinitesimal Cherednik algebras by Tsymbaliuk, Oleksandr

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On Auslander-Reiten theory for algebras and derived categories by Scherotzke, S

“…We apply these results to <em>G</em>-transitive blocks of the universal enveloping algebras of restricted <em>p</em>-Lie algebras. Finally we deduce a condition for a smash product of a local basic algebra Λ with a commutative semi-simple group algebra to have components with Euclidean tree class, in terms of the components of the Auslander-Reiten quiver of Λ.…”

Configurations in abelian categories. III. Stability conditions and identities by Joyce, D

“…Using these we define interesting (Lie) algebras of constructible functions H^{pa}_t,H^{to}_t and L^{pa}_t,L^{to}_t on Obj_A. …”

Coherent sheaves on varieties arising in Springer theory, and category 0 by Nandakumar, Vinoth

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Symplectic geometry of conical symplectic resolutions by Zivanovic, F

“…The family of Nakajima Quiver Varieties, in particular, we study in detail those of Dynkin type A; and the family of resolutions of Slodowy varieties that arise from the representation theory of semisimple Lie algebras and involve Springer theory. In the latter, we also obtain some further families of Lagrangians using Springer theoretic methods and certain crystal operators.…”

Motivic coaction on generalized hypergeometric functions by Kamlesh, D

“…There has also been recent progress, of which I am a part, that was made in collaboration with Hadleigh Frost, Martijn Hidding, Carlos Rodriguez, Oliver Schlotterer and Bram Verbeek, where we bridge the two approaches mentioned above to give a Lie algebraic reformulation of the coaction conjecture as well as applications of the new approach to computing the single-valued (trivial monodromy) map for hypergeometric functions. …”

Cayley–Klein Lie Bialgebras: Noncommutative Spaces, Drinfel’d Doubles and Kinematical Applications by Ivan Gutierrez-Sagredo, Francisco Jose Herranz

“…The Cayley–Klein (CK) formalism is applied to the real algebra <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="fraktur">so</mi><mo stretchy="false">(</mo><mn>5</mn><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> by making use of four graded contraction parameters describing, in a unified setting, 81 Lie algebras, which cover the (anti-)de Sitter, Poincaré, Newtonian and Carrollian algebras. …”
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Rough paths, kernels, differential equations and an algebra of functions on streams by Salvi, C

“…The atomic objects in a) are described via different algebraic products and using classical combinatorial objects (Hall sets) arising in the study of free Lie algebras.</p> <p>[1] Franz J Király and Harald Oberhauser. …”