Bosonic realizations of the color analogue of the Heisenberg Lie algebra

Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces I

We define the partition and $n$-point functions for a vertex operator algebra on a genus two Riemann surface formed by sewing two tori together. We obtain closed formulas for the genus two partition function for the Heisenberg free bosonic string and for any pair of simple Heisenberg modules. We prove that the partition function is holomorphic in the sewing parameters on a given suitable domain and describe its modular properties for the Heisenberg and lattice vertex operator algebras and a continuous orbifolding of the rank two fermion vertex operator super algebra. We compute the genus two H…

A note on free bosonic vertex algebra and its conformal vectors

We classify all the Heisenberg and conformal vectors and determine the full automorphism group of the free bosonic vertex algebra without gradation. To describe it we introduce a notion of inner automorphisms of a vertex algebra.

Heisenberg双的 quasi-五边形方程

A Quasi-Pentagon Equation for a Heisenberg Double of a Quasi-Hopf Algebra

本文研究了有限维 quasi-Hopf 代数的 Heisenberg 双结构，探讨了其 quasi-五边形方程和 quasi-Hopf 方程的性质。

有向图海森堡代数：预项目代数的立方类比

Quiver Heisenberg algebras: a cubic analogue of preprojective algebras

本文研究有向图海森堡代数作为预项目代数的中心扩张，探讨其在正特征下的表示理论，揭示其与路径代数的表示理论关系，并提供精确的Auslander-Reiten序列描述。

Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces II

We continue our program to define and study $n$-point correlation functions for a vertex operator algebra $V$ on a higher genus compact Riemann surface obtained by sewing surfaces of lower genus. Here we consider Riemann surfaces of genus 2 obtained by attaching a handle to a torus. We obtain closed formulas for the genus two partition function for free bosonic theories and lattice vertex operator algebras $V_L$. We prove that the partition function is holomorphic in the sewing parameters on a given suitable domain and describe its modular properties. We also compute the genus two Heisenberg v…

The Genus Two Partition Function for Free Bosonic and Lattice Vertex Operator Algebras

We define the $n$-point function for a vertex operator algebra on a genus two Riemann surface in two separate sewing schemes where either two tori are sewn together or a handle is sewn to one torus. We explicitly obtain closed formulas for the genus two partition function for the Heisenberg free bosonic string and lattice vertex operator algebras in both sewing schemes. We prove that the partition functions are holomorphic in the sewing parameters on given suitable domains and describe their modular properties. Finally, we show that the partition functions cannot be equal in the neighborhood o…