The adjoint representation inside the exterior algebra of a simple Lie algebra [PDF]
Advances in Mathematics, 2015 Final version. More misprints corrected.
Corrado De Concini +2 more
core +7 more sources
Euler's difference table and decomposition of tensor powers of adjoint representation of $A_n$ Lie algebra [PDF]
arXiv, 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. M. Perelomov
arxiv +5 more sources
Euler's triangle and the decomposition of tensor powers of adjoint representation of $A_1$ Lie algebra [PDF]
arXiv, 2019 We consider the relation between Euler's trinomial problem and the problem of decomposition of tensor powers of adjoint representation of $A_1$ Lie algebra. By using this approach, some new results for both problems are obtained.
A. M. Perelomov
arxiv +5 more sources
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
Anthony D. Joseph
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The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2010 The Hamiltonian representation for the hierarchy of Lax-type flows on a dual space to the Lie algebra of shift operators coupled with suitable eigenfunctions and adjoint eigenfunctions evolutions of associated spectral problems is found by means of a ...
Oksana Ye. Hentosh
doaj +5 more sources
Homology of the Lie algebra of vector fields on the line with coefficients in symmetric powers of its adjoint representation [PDF]
Functional Analysis and Its Applications, 2006 International ...
Vladimir Dotsenko
openalex +5 more sources
, 2023 This paper exhibits fundamental structure underlying Lie algebra homology with coefficients in tensor products of the adjoint representation, mostly focusing upon the case of free Lie algebras. The main result yields a DG category that is constructed from the PROP associated to the Lie operad.
Geoffrey Powell
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The adjoint representation of a Lie algebra and the support of Kostant's weight multiplicity formula
, 2014 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.
Pamela E. Harris +2 more
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, 2004 The space of Lie algebra cohomology is usually described by the dimensions of components of certain degree even for the adjoint module as coefficients when the spaces of cochains and cohomology can be endowed with a Lie superalgebra structure. Such a description is rather imprecise: these dimensions may coincide for cohomology spaces of distinct ...
Alexei Lebedev +2 more
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Adjoint representation of the graded Lie algebra osp(2/1; C) and its exponentiation
, 2003 We construct explicitly the grade star Hermitian adjoint representation of osp(2/1; C) graded Lie algebra. Its proper Lie subalgebra, the even part of the graded Lie algebra osp(2/1; C), is given by su(2) compact Lie algebra. The Baker-Campbell-Hausdorff formula is considered and reality conditions for the Grassman-odd transformation parameters, which ...
K. Ilyenko
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