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Fix , let be the loop Lie algebra over with basis and relations , where . In this paper, a formal distribution Lie algebra of is constructed. Then the associated conformal algebra is studied, where has a -basis with -brackets and . In particular, we determine the conformal derivations and rank one conformal modules of this conformal algebra. Finally, we study the central extensions and extensions of conformal modules. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of non-weight modules for some algebras related to the Virasoro algebra: The algebra (a, b), the twisted deformative Schrödinger-Virasoro Lie algebras and the Schrödinger algebra. We study the modules whose restriction to the Cartan subalgebra (modulo center) are free of rank 1 for these algebras. Moreover, the simplicities of these modules are determined. [ABSTRACT FROM AUTHOR]

We describe all rigid algebras and all irreducible components in the variety of four-dimensional Leibniz algebras 𝔏𝔢𝔦𝔟4 over ℂ. In particular, we prove that the Grunewald–O'Halloran conjecture is not valid and the Vergne conjecture is valid for 𝔏𝔢𝔦𝔟4. [ABSTRACT FROM AUTHOR]

Consider an inclusion of diffuse von Neumann algebras . We say that has the absorbing amenability property (AAP) if for any diffuse subalgebra and any amenable intermediate algebra we have that is contained in We prove that the cup subalgebra associated to any subfactor planar algebra has the AAP. [ABSTRACT FROM AUTHOR]