8,275 research outputs found
Realizations of Real Low-Dimensional Lie Algebras
Using a new powerful technique based on the notion of megaideal, we construct
a complete set of inequivalent realizations of real Lie algebras of dimension
no greater than four in vector fields on a space of an arbitrary (finite)
number of variables. Our classification amends and essentially generalizes
earlier works on the subject.
Known results on classification of low-dimensional real Lie algebras, their
automorphisms, differentiations, ideals, subalgebras and realizations are
reviewed.Comment: LaTeX2e, 39 pages. Essentially exetended version. Misprints in
Appendix are correcte
All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n-1
We construct all solvable Lie algebras with a specific n-dimensional
nilradical n_(n,2) (of degree of nilpotency (n-1) and with an (n-2)-dimensional
maximal Abelian ideal). We find that for given n such a solvable algebra is
unique up to isomorphisms. Using the method of moving frames we construct a
basis for the Casimir invariants of the nilradical n_(n,2). We also construct a
basis for the generalized Casimir invariants of its solvable extension s_(n+1)
consisting entirely of rational functions of the chosen invariants of the
nilradical.Comment: 19 pages; added references, changes mainly in introduction and
conclusions, typos corrected; submitted to J. Phys. A, version to be
publishe
Topological representation zeta functions of unipotent groups
Inspired by work surrounding Igusa's local zeta function, we introduce
topological representation zeta functions of unipotent algebraic groups over
number fields. These group-theoretic invariants capture common features of
established -adic representation zeta functions associated with pro-
groups derived from unipotent groups. We investigate fundamental properties of
the topological zeta functions considered here. We also develop a method for
computing them under non-degeneracy assumptions. As an application, among other
things, we obtain a complete classification of topological representation zeta
functions of unipotent algebraic groups of dimension at most six.Comment: 27 page
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