$\vee$ -Systems, Holonomy Lie Algebras, and Logarithmic Vector Fields

Lie algebras of vector fields

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Vector Fields and Nilpotent Lie Algebras

In other words, we want to write the corresponding trajectory t → x(t) in closed form. Of course, since this cannot be done for most differential equations, it is important to find a means of approximating a general flow by a flow which is explicitly integrable in closed form. In this paper we describe an infinite dimensional family of explicitly integrable flows E; in a companion paper [6] we ...

Commutant Algebras in Representations of Lie Algebras of Vector Fields

In this paper, we give an explicit description of the commutant algebras for vector fields Lie algebras Wn in their representations on Wm×n, m 6 n, which arises from the tensor product Nm CoindF n, for the basis field F of characteristic 0. The result is some analogue of Weyl’s classical reciprocity.

Lie algebras Representations and Analytic Semigroups through Dual Vector Fields

Lie Algebras of Vector Fields and Generalized Foliations

LIE ALGEBRAS OF VECTOR FIELDS AND GENERALIZED FOLIATIONS