Pseudodifferential operators are formal Laurent series in the formal inverse ∂−1 of the derivative operator ∂ whose coefficients are holomorphic functions. Given a pseudodifferential operator, the corresponding formal power series can be obtained by using some constant multiples of its coefficients. The space of pseudodifferential operators is a noncommutative algebra over C and therefore has a...

In this paper, a useful classification of all Lie subalgebras of a given Lie algebraup to an inner automorphism is presented. This method can be regarded as animportant connection between differential geometry and algebra and has many applications in different fields of mathematics. After main results, we have applied this procedure for classifying the Lie subalgebras of some examples of Lie al...

Conformal algebra is an axiomatic description of the operator product expansion (or rather its Fourier transform) of chiral fields in a conformal field theory. It turned out to be an adequate tool for the realization of the program of the study of Lie (super)algebras and associative algebras (and their representations), satisfying the sole locality property [K3]. The first basic definitions and...

Conformal algebra is an axiomatic description of the operator product expansion (or rather its Fourier transform) of chiral fields in a conformal field theory. It turned out to be an adequate tool for the realization of the program of the study of Lie (super)algebras and associative algebras (and their representations), satisfying the sole locality property [K3]. The first basic definitions and...

In this paper, by using of Frobenius theorem a relation between Lie subalgebras of the Lie algebra of a top space T and Lie subgroups of T(as a Lie group) is determined. As a result we can consider these spaces by their Lie algebras. We show that a top space with the finite number of identity elements is a C^{∞} principal fiber bundle, by this method we can characterize top spaces.

This is a list of published papers on series of Lie groups. It is intended to be complete but no doubt there are omissions. There are unpublished omissions. The principal ones are the papers by Pierre Vogel. These are available on his home page as zipped postscript files. The url is http://www.institut.math.jussieu.fr/ vogel/ Prpublications / Preprints Algebraic structure on modules of diagrams...

The Segal-Bargmann transform plays an important role in quantum theories of linear fields. Recently, Hall obtained a non-linear analog of this transform for quantum mechanics on Lie groups. Given a compact, connected Lie group G with its normalized Haar measure μH , the Hall transform is an isometric isomorphism from L (G,μH ) to H(GC) ∩ L2(GC, ν), where GC the complexification of G, H(GC) the ...

Locally extended affine Lie algebras were introduced by Morita and Yoshii in [J. Algebra 301(1) (2006), 59-81] as a natural generalization of extended affine Lie algebras. After that, various generalizations of these Lie algebras have been investigated by others. It is known that a locally extended affine Lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

Given a formal power series f(z) ∈ C[[z]] we define, for any positive integer r, its rth Witt transform, W (r) f , by W (r) f (z) = 1 r ∑ d|r μ(d)f(z d)r/d, where μ denotes the Möbius function. The Witt transform generalizes the necklace polynomials, M(α;n), that occur in the cyclotomic identity 1 1− αy = ∞