The adjoint representation inside the exterior algebra of a simple Lie algebra [PDF]
Advances in Mathematics, 2015 Final version. More misprints corrected.
DE CONCINI, Corrado +2 more
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Characterizing barren plateaus in quantum ansätze with the adjoint representation. [PDF]
Nat Commun, 2023 Variational quantum algorithms, a popular heuristic for near-term quantum computers, utilize parameterized quantum circuits which naturally express Lie groups.
Fontana E +7 more
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Multiplicity of the Adjoint Representation in Simple Quotients of the Enveloping Algebra of a Simple Lie Algebra [PDF]
Transactions of the American Mathematical Society, 1989 Let g \mathfrak {g} be a complex simple Lie algebra, h \mathfrak {h} a Cartan subalgebra and U ( g ) U(\mathfrak {g}) the enveloping algebra of g \mathfrak {g} . We calculate for each maximal two-sided
A. Joseph
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The adjoint representation of a Lie algebra and the support of Kostant's weight multiplicity formula
, 2013 Even though weight multiplicity formulas, such as Kostant's formula, exist their computational use is extremely cumbersome. In fact, even in cases when the multiplicity is well understood, the number of terms considered in Kostant's formula is factorial in the rank of the Lie algebra and the value of the partition function is unknown.
Harris, Pamela E. +2 more
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Useful relations among the generators in the defining and adjoint representations of SU(N)
SciPost Physics Lecture Notes, 2021 There are numerous relations among the generators in the defining and adjoint representations of SU(N). These include Casimir operators, formulae for traces of products of generators, etc.
Howard E. Haber
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Euler’s difference table and the decomposition of tensor powers of the adjoint representation of the $$A_n$$ Lie algebra [PDF]
Theoretical and mathematical physics, 2019 By using of Euler's difference table, we obtain simple explicit formula for the decomposition of $k$-th tensor power of adjoint representation of $A_n$ Lie algebra at $2 k \le{n+1}$.
A. Perelomov
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Kupershmidt-(dual-)Nijenhuis structures on a Lie algebra with a representation [PDF]
Journal of Mathematics and Physics, 2018 In this paper, first we study infinitesimal deformations of a Lie algebra with a representation and introduce the notion of a Nijenhuis pair, which gives a trivial deformation of a Lie algebra with a representation.
Y. Hu, Jiefeng Liu, Y. Sheng
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Deformations of the three-dimensional Lie algebra sl(2)
Қарағанды университетінің хабаршысы. Математика сериясы, 2020 Deformation is one of key questions of the structural theory of algebras over a field. Especially, it plays a important role in the classification of such algebras.
A.A. Ibrayeva +2 more
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Results in Physics, 2023 Introduction:: The chemical oscillators are identified as open system that demonstrate periodic changes in the concentration of some reaction species as a result of intricate physico-chemical mechanisms which can lead to bi-stability, the occurrence of ...
Ebrahem A. Algehyne +4 more
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Entropy, 2016 We introduce the symplectic structure of information geometry based on Souriau’s Lie group thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances through co-adjoint action of a group on its moment space, defining physical ...
Frédéric Barbaresco
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