InforLorV4, Main, Exploration, bibRecord, 00B365

Formal power series, operator calculus, and duality on Lie algebras

Identifieur interne : 00B365 ( Main/Exploration ); précédent : 00B364; suivant : 00B366

Formal power series, operator calculus, and duality on Lie algebras

Auteurs : Philip Feinsilver [États-Unis] ; René Schott [France]

Source :

Discrete Mathematics [ 0012-365X ] ; 1998.

RBID : ISTEX:3B429CE2B5DF18EE4989874B34D6AE39399EC50E

English descriptors

Teeft :
- Adjoint, Adjoint representation, Algebra, Associative algebra, Basis elements, Calculus, Coadjoint orbits, Commutation relations, Computer science, Control optim, Control theory, Differential operator, Discrete volterra series, Dual representations, Exponential, Feinsilver, Formal power series, Formal series, General hamiltonian, Group element, Initial conditions, Iterated integrals, Lecture notes, Local controllability, Matrix, Nonlinear control theory, Operator calculus, Operator calculus approach, Partial derivatives, Power sums, Principal matrices, Probability theory, Product formulation, Right action, Robotic manipulation, Schott, Schottldiscrete mathematics, Second kind, Smooth functions, Splitting lemma, Survival analysis, Vector fields, Volterra, Volterra product, Volterra series.

Abstract

Abstract: This paper presents an operator calculus approach to computing with non-commutative variables. First, we recall the product formulation of formal exponential series. Then we show how to formulate canonical boson calculus on formal series. This calculus is used to represent the action of a Lie algebra on its universal enveloping algebra. As applications, Hamilton's equations for a general Hamiltonian, given as a formal series, are found using a double-dual representation, and a formulation of the exponential of the adjoint representation is given. With these techniques one can represent the Volterra product acting on the enveloping algebra. We illustrate with a three-step nilpotent Lie algebra.

Url:

https://api.istex.fr/ark:/67375/6H6-4V89CKM4-R/fulltext.pdf

DOI: 10.1016/S0012-365X(97)00113-1

Affiliations:

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Le document en format XML

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Formal power series, operator calculus, and duality on Lie algebras

Formal power series, operator calculus, and duality on Lie algebras

Source :

English descriptors

Abstract

Links toward previous steps (curation, corpus...)

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri