Results 1 to 10 of about 139,367 (266)
Characterizing barren plateaus in quantum ansätze with the adjoint representation [PDF]
Nature CommunicationsVariational 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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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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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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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.
Eric M. Friedlander, Brian Parshall
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A representation for an adjoint operator
Journal of Numerical Analysis and Approximation Theory, 1975 Not available.
Stephen P. Travis
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Torus knots in adjoint representation and Vogel’s universality
European Physical Journal C: Particles and FieldsVogel’s universality gives a unified description of the adjoint sector of representation theory for simple Lie algebras in terms of three parameters $$\alpha ,\beta ,\gamma $$ α , β , γ , which are homogeneous coordinates of Vogel’s plane.
Liudmila Bishler, Andrei Mironov
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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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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 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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