Search results for "ILTER"
showing 10 items of 1040 documents
Integral curves of derivations
1988
We integrate, by a constructive method, derivations of even degree on the sections of an exterior bundle by families of Z 2-graded algebra automorphisms, dependent on a real parameter, and which satisfy a flow condition. We also study the case of local endomorphisms when their components of degree zero and derivations and with no component of negative degree, but then we have integral families of R-linear automorphisms. This integration method can be applied to the Frolicher—Nijenhuis derivations on the Cartan algebra of differential forms, and to the integration of superfields on graded manifolds.
An Introduction to Geometric Algebra and Conics
2016
This chapter introduces the conics and characterizes them from an algebraic perspective. While in depth geometrical aspects of the conics lie outside the scopes of this chapter, this chapter is an opportunity to revisit concepts studied in other chapters such as matrix and determinant and assign a new geometric characterization to them.
Affine varieties and lie algebras of vector fields
1993
In this article, we associate to affine algebraic or local analytic varieties their tangent algebra. This is the Lie algebra of all vector fields on the ambient space which are tangent to the variety. Properties of the relation between varieties and tangent algebras are studied. Being the tangent algebra of some variety is shown to be equivalent to a purely Lie algebra theoretic property of subalgebras of the Lie algebra of all vector fields on the ambient space. This allows to prove that the isomorphism type of the variety is determinde by its tangent algebra.
Algebras of pseudodifferential operators on complete manifolds
2003
In several influential works, Melrose has studied examples of non-compact manifolds M 0 M_0 whose large scale geometry is described by a Lie algebra of vector fields V ⊂ Γ ( M ; T M ) \mathcal V \subset \Gamma (M;TM) on a compactification of M 0 M_0 to a manifold with corners M M . The geometry of these manifolds—called “manifolds with a Lie structure at infinity”—was studied from an axiomatic point of view in a previous paper of ours. In this paper, we define and study an algebra Ψ 1 , 0 , V ∞ ( M 0 ) \Psi _{1,0,\mathcal V}^\infty (M_0) of pseudodifferential operators canonically associated to a manifold M 0 M_0 with a Lie structure at infinity V ⊂ Γ ( M ; T M ) \mathcal V \subset \Gamma (…
The graded identities of upper triangular matrices of size two
2002
AbstractLet UT2 be the algebra of 2×2 upper triangular matrices over a field F. We first classify all possible gradings on UT2 by a group G. It turns out that, up to isomorphism, there is only one non-trivial grading and we study all the graded polynomial identities for such algebra. In case F is of characteristic zero we give a complete description of the space of multilinear graded identities in the language of Young diagrams through the representation theory of the hyperoctahedral group. We finally establish a result concerning the rate of growth of the identities for such algebra by proving that its sequence of graded codimensions has almost polynomial growth.
An extension of the algebra of sets
1973
We shall explain the aim which leads us in the construction of an extended system of the algebra of sets1. The symbol 1. {*:?(*)} denoting the set of these and only these elements of domain of the variable x which satisfy the propositional condition (propositional function or form) ?9 (x)" is in com? mon use nowadays, so that it is adopted in school courses of mathematics in many countries, and in Poland as well. This condition will be said to define the set 1. However, if we admit propositional conditions which are meaningless for some values of their variables then we encounter some difficulties connected with the ex? pression 1. The formulae 2. {x : 9 (*)} = {x : 9 (*)}' 3. {x : 9 (s) v …
POLYNOMIAL IDENTITIES ON SUPERALGEBRAS AND ALMOST POLYNOMIAL GROWTH
2001
Let A be a superalgebra over a field of characteristic zero. In this paper we investigate the graded polynomial identities of A through the asymptotic behavior of a numerical sequence called the sequence of graded codimensions of A. Our main result says that such sequence is polynomially bounded if and only if the variety of superalgebras generated by A does not contain a list of five superalgebras consisting of a 2-dimensional algebra, the infinite dimensional Grassmann algebra and the algebra of 2 × 2 upper triangular matrices with trivial and nontrivial gradings. Our main tool is the representation theory of the symmetric group.
Graded polynomial identities and Specht property of the Lie algebrasl2
2013
Abstract Let G be a group. The Lie algebra sl 2 of 2 × 2 traceless matrices over a field K can be endowed up to isomorphism, with three distinct non-trivial G-gradings induced by the groups Z 2 , Z 2 × Z 2 and Z . It has been recently shown (Koshlukov, 2008 [8] ) that for each grading the ideal of G-graded identities has a finite basis. In this paper we prove that when char ( K ) = 0 , the algebra sl 2 endowed with each of the above three gradings has an ideal of graded identities Id G ( sl 2 ) satisfying the Specht property, i.e., every ideal of graded identities containing Id G ( sl 2 ) is finitely based.
The Virasoro Algebra
1989
In this chapter we shall study the Lie algebra Vect S1 of vector fields on a circle and some of its generalizations. The Lie algebra Vect S1 has a central extension, the Virasoro algebra. The representation theory of the Virasoro algebra is closely related to the representation theory of affine Lie algebras. In fact, through the Sugawara construction, to be defined below, a highest weight representation of an affine Lie algebra carries always a highest weight representation of the Virasoro algebra. All the irreducible highest weight representations of the Virasoro algebra are known and they can be exponentiated to representations of associated infinite-dimensional Lie groups. The representa…
The Bohm-Aharonov effect: A seven-dimensional structural group
1996
We realize a nonfaithful representation of a seven-dimensional Lie algebra, the extension of which to its universal enveloping algebra contains most of the observables of the scattering Aharonov-Bohm effect, as essentially self-adjoint operators: the scattering Hamiltonian, the total and kinetic angular momenta, the positions and the kinetic momenta. By restriction, we obtain the model introduced in Lett. Math. Phys.1 (1976), 155–163.