Results 11 to 20 of about 139,367 (266)
On the Stiefel-Whitney class of the adjoint representation of $E_8$ [PDF]
Kyoto Journal of Mathematics, 2004 Let \(\widetilde{E_8}\) be the \(3\)-connected covering space of the simply connected Lie group \(E_8\). Let \(\pi_8: \widetilde{E_8} \to E_8\) be the covering map and \(\pi_8^*: H^*(Be_8) \to H^*(B\widetilde{E_8})\) be the induced map between the \(\mathbb{Z}_2\) cohomology of the classifying spaces.
Akihiro Ohsita
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Lie Supergroups Obtained from 3-Dimensional Lie Superalgebras Associated to the Adjoint Representation and Having a 2-Dimensional Derived Ideal [PDF]
International Journal of Mathematics and Mathematical Sciences, 2008 We give the explicit multiplication law of the Lie supergroups for which the base manifold is a 3-dimensional Lie group and whose underlying Lie superalgebra g=g0⊕g1 which satisfies g1=g0, g0 acts on g1 via the adjoint representation and g0 has a 2 ...
I. Hernández, R. Peniche
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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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On the adjoint representation of a hopf algebra [PDF]
Proceedings of the Edinburgh Mathematical Society, 2020 AbstractWe consider the adjoint representation of a Hopf algebra $H$ focusing on the locally finite part, $H_{{\textrm ad\,fin}}$, defined as the sum of all finite-dimensional subrepresentations. For virtually cocommutative $H$ (i.e., $H$ is finitely generated as module over a cocommutative Hopf subalgebra), we show that $H_{{\textrm ad\,fin}}$ is a ...
Kolb S, Lorenz M, Nguyen B, Yammine R
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Simultaneous representation by adjoint quadratic forms [PDF]
Acta Arithmetica, 1964 Gordon Pall
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Representations are adjoint to endomorphisms [PDF]
Journal of Homotopy and Related Structures, 2019 The functor that takes a ring to its category of modules has an adjoint if one remembers the forgetful functor to abelian groups: the endomorphism ring of linear natural transformations. This uses the self-enrichment of the category of abelian groups. If one considers enrichments into symmetric sequences or even bisymmetric sequences, one can produce ...
Joseph Hirsh +2 more
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Worldline description of a bi-adjoint scalar and the zeroth copy
Journal of High Energy Physics, 2021 Bi-adjoint scalars are helpful in studying properties of color/kinematics duality and the double copy, which relates scattering amplitudes of gauge and gravity theories. Here we study bi-adjoint scalars from a worldline perspective.
Fiorenzo Bastianelli +2 more
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An adjoint representation for polynomial algebras [PDF]
Proceedings of the American Mathematical Society, 1987 This paper shows that a graded polynomial algebra over F 2 {F_2} with Steenrod algebra action possesses an analog of the adjoint representation for the cohomology of the classifying space of a compact connected Lie group.
Robert E. Stong, Stephen A. Mitchell
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GMOR relation for a QCD-like theory from S-duality
Physics Letters B, 2022 Following [1] we study a QCD-like gauge theory using a non-supersymmetric setup in type IIB string theory. The setup includes an O3 plane and N D3 anti-branes and it realises a USp(2N) ‘electric’ gauge theory with four “quarks” in the two-index ...
Adi Armoni, Henry Harper-Gardner
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Universal Racah matrices and adjoint knot polynomials: Arborescent knots
Physics Letters B, 2016 By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras.
A. Mironov, A. Morozov
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