Results 1 to 10 of about 1,612,052 (325)
A category for the adjoint representation [PDF]
Journal of Algebra, 2000 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
Huerfano, Ruth Stella, Khovanov, Mikhail
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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
arxiv +11 more sources
Characterizing barren plateaus in quantum ansätze with the adjoint representation [PDF]
Nature Communications, 2023 Variational quantum algorithms, a popular heuristic for near-term quantum computers, utilize parameterized quantum circuits which naturally express Lie groups.
Enrico Fontana +7 more
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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
semanticscholar +7 more sources
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
openalex +10 more sources
A representation for an adjoint operator
Journal of Numerical Analysis and Approximation Theory, 1975 Not available.
Stephen P. Travis
doaj +3 more sources
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
doaj +2 more sources
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 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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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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