Pilar Benito, Javier Rández-Ibáñez, Jorge Roldán-López
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引用次数: 0
Abstract
The procedure of double extension of vector spaces endowed with non-degenerate bilinear forms allows us to introduce the class of generalized \(\mathbb {K}\)-oscillator algebras over an arbitrary field \(\mathbb {K}\). Starting from basic structural properties and the canonical forms of skew-adjoint endomorphisms, we will proceed to classify the subclass of quadratic nilpotent algebras and characterize those algebras with quadratic dimension 2. This will enable us to recover the classification of real oscillator algebras, a.k.a Lorentzian algebras, given by Medina et al. (Ann Sci École Norm Sup 18:553–561, 1985).
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
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