Results 1 to 10 of about 317,803 (230)
A Category for the Adjoint Representation
Journal of Algebra, 2001 We construct an abelian category C and exact functors in C which on the Grothendieck group descend to the action of a simply-laced quantum group in its adjoint representation. The braid group action in the adjoint representation lifts to an action in the derived category of C.
Ruth Stella Huerfano, Mikhail Khovanov
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The canonical basis of the quantum adjoint representation [PDF]
arXiv, 2016 We identify the canonical basis of the quantum adjoint representation of a quantized enveloping algebra with a basis that we defined before the theory of canonical bases was available.
G. Lusztig
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Adjoints and low-rank covariance representation [PDF]
Nonlinear Processes in Geophysics, 2001 Abstract. Quantitative measures of the uncertainty of Earth system estimates can be as important as the estimates themselves. Direct calculation of second moments of estimation errors, as described by the covariance matrix, is impractical when the number of degrees of freedom of the system state is large and the sources of uncertainty are not ...
Michael K. Tippett, Stephen E. Cohn
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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 1-connected, compact exceptional group $E_8$, which is regarded as the loop space of the homotopy fibre $B\widetilde{E}_8$ of a map from $BE_8$, the classifying space of $E_8$, to an Eilenberg-MacLane space.
Akihiro Ohsita
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The spectrum of the adjoint representation and the hyperbolicity of dynamical systems
Journal of Differential Equations, 1980 Let (M,g) denote a smooth compact Riemannian manifold. Anosov [I] defined the global hypcrbolicity of a C2 diffeomorphism (resp. a nonsingular flow f’) on M :f (resp. fr) is h yperbolic or, as we shall say, Anosov, if the tangent bundle TM splits as a sum of invariant subbundles TM = E’ ~3 E(resp. TM = B @ E@ [A’, where [X7 is th I e ine bundle spanned
Carmen Chicone, R. C. Swanson
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On the geometry of the adjoint representation of a Chevalley group
Journal of Algebra, 1989 AbstractWe prove that the adjoint module of a Chevalley group (not of type Cl) has a presentation by long root subalgebras, subject to certain relations determined by the minimal parabolic subgroups.
Helmut Völklein
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Decomposition of the Adjoint Representation of the Small Quantum sl 2 [PDF]
Communications in Mathematical Physics, 1997 Given a finite type root datum and a primitive root of unity $q=\sqrt[l]{1}$, G.~Lusztig has defined in [Lu] a remarkable finite dimensional Hopf algebra $\fu$ over the cyclotomic field ${\Bbb Q}(\sqrt[l]{1})$. In this note we study the adjoint representation $\ad$ of $\fu$ in the simplest case of the root datum $sl_2$.
Viktor Ostrik
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The Adjoint Representation of a Higher Lie Groupoid [PDF]
arXiv, 2023 We extend the standard construction of the adjoint representation of a Lie groupoid to the case of an arbitrary higher Lie groupoid. As for a Lie groupoid, the adjoint representation of a higher Lie groupoid turns out to be a representation up to homotopy which is well defined up to isomorphism.
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Transformation groups resembling the adjoint representation [PDF]
Proceedings of the American Mathematical Society, 1975 If G G is a compact, connected Lie group, the isotropy subgroups of the adjoint representation of G G are connected and the dimension of the fixed point set of a maximal torus of G G is equal to the the rank of G G . Results similar to these are given when G G acts
R.W. Sullivan
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Rational actions associated to the adjoint representation [PDF]
Annales scientifiques de l'École normale supérieure, 1987 Eric M. Friedlander, Brian Parshall
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