Possible central extensions of non-relativistic conformal algebras in 1+1

In this paper, we study a class of Leibniz conformal algebras called quadratic Leibniz conformal algebras. An equivalent characterization of a Leibniz conformal algebra [Formula: see text] through three algebraic operations on [Formula: see text] is given. By this characterization, several constructions of quadratic Leibniz conformal algebras are presented. Moreover, one-dimensional central extensions of quadratic Leibniz conformal algebras are considered using some bilinear forms on [Formula: see text]. In particular, we also study one-dimensional Leibniz central extensions of quadratic Lie conformal algebras.

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Structure of a Class of Rank Two Lie Conformal Algebras

Algebra Colloquium ◽

10.1142/s1005386721000158 ◽

2021 ◽

Vol 28 (01) ◽

pp. 169-180

Author(s):

Wei Wang ◽

Chunguang Xia

Keyword(s):

Complex Number ◽

Central Extensions ◽

Conformal Algebras ◽

Rank One

Let [Formula: see text] be a complex number, and a class of non-semisimple and non-solvable rank two Lie conformal algebras [Formula: see text] are introduced. In this paper, conformal derivations, conformal quasiderivations, generalized conformal derivations and conformal biderivations of [Formula: see text] are studied. Besides, central extensions and conformal modules of rank one of [Formula: see text] are determined.

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Existentially closed central extensions of locally finite p-groups

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100066093 ◽

1986 ◽

Vol 100 (2) ◽

pp. 281-301 ◽

Cited By ~ 5

Author(s):

Felix Leinen ◽

Richard E. Phillips

Keyword(s):

Central Extensions ◽

Locally Finite ◽

Existentially Closed ◽

Image Position

Throughout, p will be a fixed prime, and will denote the class of all locally finite p-groups. For a fixed Abelian p-group A, we letwhere ζ(P) denotes the centre of P. Notice that A is not a class in the usual group-theoretic sense, since it is not closed under isomorphisms.

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