Both the basic cohomology groups and the reduced cohomology groups of the Schrödinger-Virasoro conformal algebra with trivial coefficients are completely determined.
Lie conformal algebras W(a, b) are the semi-direct sums of Virasoro Lie conformal algebra and its nontrivial conformal modules of rank one. In this paper, we give a complete classification of extensions of finite irreducible conformal modules of W(a, b). With a similar method, we characterize all extensions of finite irreducible conformal modules of Schrödinger-Virasoro type Lie conformal algebras T SV (a, b) and T SV (c).
In this paper, we obtain a class of Z-graded conformal algebras which is induced by Heisenberg-Virasoro conformal algebra. More precisely, we classify Z-graded conformal algebrasFurther, we prove that all finite nontrivial irreducible modules of these algebras under some special conditions are free of rank one as a C[∂]-module. The conformal derivations of this class of graded Lie conformal algebras are also determined.
In this paper, we introduce a {λ1→n−1}-bracket and a distribution notion of an n-Lie conformal algebra. For any n-Lie conformal algebra R, there exists a series of associated infinite-dimensional linearly compact n-Lie algebras {(L iep R) } (p≥1) . We show that torsionless finite n-Lie conformal algebras R and S are isomorphic if and only if (L iep R) ≃ (L iep S) as linearly compact n-Lie algebras with ∂t i -action for any p ≥ 1. Moreover, the representation and cohomology theory of n-Lie conformal algebras are established. In particular, the complex of R is isomorphic to a subcomplex of n-Lie algebra (L iep R) .
An approach that can be used to generate more complex and interesting optical fields is proposed by controlling the phase, position, size and amplitude of each coherent array. To illustrate the advantages of the approach, the power coupling efficiency of the optical systems with Cassegrain-telescope receivers is studied. It shows that the approach exhibits greater advantage over traditional coherent combining beams.
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