arXiv subjects

Ryo Hayami

Publications and source records attributed to Ryo Hayami.

3 recordsLinked to original sources

arXiv2026

Quandles from gauge transformations

In this paper, we investigate a quandle structure induced by an augmented rack arising from a gauge transformation group. We construct a quandle from a principal bundle and its discrete generalization. When we see a group as a (discrete) principal bundle over a point, this quandle becomes equivalent to the generalized Alexander quandle for its inner automorphism. Moreover, we construct a Lie and Noether quandle structure from a smooth gauge transformation.

math.GR↗

arXiv2025

An integration of Lie-Leibniz triples

In this paper, we introduce the group version of a Lie-Leibniz triple, which we call a Lie group-rack triple. We define a Lie group-rack triple whose tangent structure is a Lie-Leibniz triple, which is a generalization of an augmented Lie rack whose tangent structure is an augmented Leibniz algebra. We show that any finite-dimensional Lie-Leibniz triple can be integrated to a local Lie group-rack triple by generalizing the integration procedure of an augmented Leibniz algebra into an augmented Lie rack.

math.DG↗

arXiv2023

Higher Courant-Dorfman algebras and associated higher Poisson vertex algebras

In this paper, we consider a notion of a higher version of the relation between Courant-Dorfman algebras and Poisson vertex algebras. We define a higher Courant-Dorfman algebra, and study the relationship with graded symplectic geometry. In particular, we give graded Poisson algebras of degree $-n$ in the non-degenerate case. For higher Courant-Dorfman algebras coming from finite-dimensional vector bundles, they coincide with the algebras of functions of the associated differential-graded(dg) symplectic manifolds of degree $n$. We define a higher Lie conformal algebra and Poisson vertex algebra, and give a higher (weak) Courant-Dorfman algebraic structure arising from them. Moreover, we prove that the higher Lie conformal algebras and higher Poisson vertex algebras have properties like Lie conformal algebras and Poisson vertex algebras. As an example, we obtain an algebraic description of Batalin-Fradkin-Vilkovisky(BFV) current algebras.

math-ph↗