Results 11 to 20 of about 2,880 (181)
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.
Huerfano, Ruth Stella, Khovanov, Mikhail
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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 ...
Tippett, M. K., Cohn, S. E.
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Rational actions associated to the adjoint representation [PDF]
Annales scientifiques de l'École normale supérieure, 1987 Let \(G\) be a simple algebraic group with Lie algebra \(\mathfrak g\). In this paper the authors prove a \(G\)-equivariant version of the Poincaré-Birkhoff-Witt theorem. In positive characteristic they also obtain analogous results for the hyperalgebras of \(G\) and of the Frobenius kernels \(G_r\), \(r\geq 1\). Extending \textit{F. D.
Brian Parshall, Eric M. Friedlander
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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
R. C. Swanson, Carmen Chicone
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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.
Department of Mathematics, University of Florida, Gainesville, Florida 32611 U.S.A. ( host institution ) +1 more
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The canonical basis of the quantum adjoint representation [PDF]
Journal of Combinatorial Algebra, 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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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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On the Stiefel-Whitney classes 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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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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