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[en] The l-conformal extension of the Newton-Hooke algebra proposed in [J. Negro, M.A. del Olmo, A. Rodriguez-Marco, J. Math. Phys. 38 (1997) 3810] is formulated in the basis in which the flat space limit is unambiguous. Admissible central charges are specified. The infinite-dimensional Virasoro-Kac-Moody type extension is given.
[en] We study the endomorphisms of idempotent medial quasigroups and determinability of some classes of medial quasigroups by their endomorphisms. We introduce the endomorphism algebra of idempotent medial quasigroup and prove that if the endomorphism algebras of quasigroups are isomorphic, then the corresponding quasigroups are isomorphic as well. In addition, we present a counterexample to demonstrate that the endomorphism algebras can not be replaced by the endomorphism monoids.
[en] It is shown that the infinite parameter gauge superalgebras of the conformal and of the N=1 Einstein supergravities can be obtained as the closures of various two finite-parameter superalgebras. In the conformal case the standard, minimal and Einsteinian closures are studied. In the case of the N=1 Einstein supergravities the minimal and non-minimal closures are discussed. (author)
[en] Classification of rational conformal field theories is essentially equivalent to classification of all possible four-point functions for the primary fields of the theories. An interesting set of parameters appearing in the latter classification is given by the number and the positions of so-called apparent singularities of the differential equations which are obeyed by the four-point functions. The subject of this paper is a detailed analysis of the role played by these parameters. In particular the restrictions imposed on them by general principles of two-dimensional conformal field theory are worked out, and the implications on the classification programme are discussed. (author). 46 refs
[en] The method of induced representations is applied to the conformal group. By its means, it is shown that the coset space to be used within the coset space technique for the construction of conformally-invariant theories must include the “Nambu-Goldstone” fields for special conformal transformations. They turn out to be non-dynamical fields whose dependence on the coordinates is fixed by the symmetries.
[en] The conditions for N=2,4,8 supersymmetric extensions of the N=1 superconformal Kac-Moodi current algebras are studied. The correspondence between the N=2 and 4 superconformal Kac-Moodi algebras and finite-dimensional Manin triples is found
[en] The Lie conformal algebra of loop Virasoro algebra, denoted by CW, is introduced in this paper. Explicitly, CW is a Lie conformal algebra with C[∂]-basis (Li | i∈Z) and λ-brackets [Li λ Lj] = (−∂−2λ)Li+j. Then conformal derivations of CW are determined. Finally, rank one conformal modules and Z-graded free intermediate series modules over CW are classified
[en] It is shown that N-Galilean conformal algebra with N odd and nontrivial central charge is the maximal symmetry algebra for higher derivative free theory both on classical and quantum levels. By maximal symmetry algebra the Lie algebra of the maximal group of space–time symmetry transformations is understood which preserves higher order free dynamics
[en] We consider the embedding method of the superconformal group in four dimensions in the case of extended supersymmetry, hence generalizing the recent work of Goldberger, Skiba and Son which was restricted at N=1. Moreover, we work out explicitly the case of N=2 chiral superfields in four dimensions, putting the component fields in correspondence with Pascal's pyramid at layer N. This correspondence is a generic property of the N-extended chiral sector.