SIMPLE WEAK MODULES FOR THE FIXED POINT SUBALGEBRA OF THE HEISENBERG VERTEX OPERATOR ALGEBRA OF RANK 1 BY AN AUTOMORPHISM OF ORDER 2 AND WHITTAKER VECTORS

Tanabe Kenichiro

首页> 外文期刊>Proceedings of the American Mathematical Society >SIMPLE WEAK MODULES FOR THE FIXED POINT SUBALGEBRA OF THE HEISENBERG VERTEX OPERATOR ALGEBRA OF RANK 1 BY AN AUTOMORPHISM OF ORDER 2 AND WHITTAKER VECTORS

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SIMPLE WEAK MODULES FOR THE FIXED POINT SUBALGEBRA OF THE HEISENBERG VERTEX OPERATOR ALGEBRA OF RANK 1 BY AN AUTOMORPHISM OF ORDER 2 AND WHITTAKER VECTORS

机译：HEISENBERG顶点算子代数的固定点子晶句的简单弱模块由订单2和WHittaker矢量的自同一级别

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Let M(1) be the vertex operator algebra with the Virasoro element omega associated to the Heisenberg algebra of rank 1 and let M(1)(+) be the subalgebra of M(1) consisting of the fixed points of an automorphism of M(1) of order 2. We classify the simple weak M(1)(+)-modules with a non-zero element w such that for some integer s >= 2, omega(i)w is an element of C-w (i = left perpendiculars/2right perpendicular + 1, left perpendiculars/2right perpendicular + 2,..., s - 1), omega(s)w is an element of C(x)w, and omega(i)w = 0 for all i > s. The result says that any such simple weak M(1)(+)-module is isomorphic to some simple weak M(1)-module or to some theta-twisted simple weak M(1)-module.

机译：让m（1）是与virasoro元素omega与秩1的Heisenberg代数相关联的Virasoro元素omega，让m（1）（+）是m（1）的子晶代，由m的自动形态的固定点组成（1）订单2.我们将简单的弱m（1） - 模块分类为非零元素w，使得对于某些整数s> = 2，Omega（i）w是CW的一个元素（i =左侧垂直/ 2缘垂直+ 1，左垂直/ 2缘垂直+ 2，...，S-1），Omega（S）W是C（x）w，ω（i）w = 0的元素所有我> s。结果表明，任何这种简单的弱M（1）（+） - 模块是一些简单的弱M（1）-module或者一些TheTa扭曲的简单弱M（1）-module。

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《Proceedings of the American Mathematical Society》 |2017年第10期|共14页
作者
Tanabe Kenichiro;
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作者单位

Hokkaido Univ Dept Math Kita Ku Kita 10 Nishi 8 Sapporo Hokkaido 0600810 Japan;

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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Vertex operator algebras; weak modules; Whittaker vectors;

机译：顶点操作员代数;弱模块;惠特柜矢量;

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1. SIMPLE WEAK MODULES FOR THE FIXED POINT SUBALGEBRA OF THE HEISENBERG VERTEX OPERATOR ALGEBRA OF RANK 1 BY AN AUTOMORPHISM OF ORDER 2 AND WHITTAKER VECTORS [J] . Tanabe Kenichiro Proceedings of the American Mathematical Society . 2017,第10期

机译：HEISENBERG顶点算子代数的固定点子晶句的简单弱模块由订单2和WHittaker矢量的自同一级别
2. The irreducible weak modules for the fixed point subalgebra of the vertex algebra associated to anon-degenerate even lattice by an automorphism of order 2 (Part 1) [J] . Tanabe Kenichiro Journal of Algebra . 2021,第1期

机译：通过订单2（第1部分）与Anon-Reaperate甚至晶格相关联的顶点代数的固定点子晶片的不可缩短的模块（第1部分）
3. SIMPLE WHITTAKER MODULES OVER FREE BOSONIC ORBIFOLD VERTEX OPERATOR ALGEBRAS [J] . Hartwig Jonas T., Yu Nina Proceedings of the American Mathematical Society . 2019,第8期

机译：简单的惠花模块在免费的博斯尼管orbifold顶点算子代数
4. Twisted modules and quasi-modules for vertex operator algebras [C] . Haisheng Li International Conference on Lie Algebras, Vertex Operator Algebras and Their Applications . 2007

机译：扭曲模块和顶点操作员代数的模块
5. Whittaker modules for Heisenberg and affine Lie algebras. [D] . Christodoulopoulou, Konstantina. 2007

机译：用于海森堡和仿射李代数的Whittaker模块。
6. Rota–Baxter operators and post-Lie algebra structures on semisimple Lie algebras [O] . Dietrich Burde, Vsevolod Gubarev -1

机译：半简单李代数上的Rota–Baxter算子和后李代数结构
7. The irreducible weak modules for the fixed point subalgebra of the vertex algebra associated to a non-degenerate even lattice by an automorphism of order 2 (Part 1) [O] . Kenichiro Tanabe 2021

机译：通过订单2的自同网（第1部分）与非退化均匀格子相关联的顶点代数的固定点子晶片的不可缩短模块（第1部分）

SIMPLE WEAK MODULES FOR THE FIXED POINT SUBALGEBRA OF THE HEISENBERG VERTEX OPERATOR ALGEBRA OF RANK 1 BY AN AUTOMORPHISM OF ORDER 2 AND WHITTAKER VECTORS

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