Scholarlink

<p>We propose a construction of a double quasi-Poisson bracket on the group algebra associated to the twisted fundamental group of a marked oriented surface (<i>S</i>,&#xa0;<i>P</i>) with boundary, where <i>P</i> is a finite set of marked points on the boundary of the surface <i>S</i> such that on every boundary component there is at least one point of <i>P</i>. We show that this double bracket is a noncommutative generalization of the well-known Goldman bracket, defined on the space of free homotopy classes of loops on <i>S</i>. For an algebra <i>A</i> without polynomial identities, we construct a double bracket on the space of decorated twisted <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({{\,\textrm{GL}\,}}_n(A)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mrow> <mspace width="0.166667em" /> <mtext>GL</mtext> <mspace width="0.166667em" /> </mrow> <mi>n</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>-, symplectic and indefinite orthogonal local systems.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On double brackets for marked surfaces

  • 期刊论文

  • 发表日期：

    2026年2月10日

查看全文
  • Michael Gekhtman,
  • Eugen Rogozinnikov

摘要

We propose a construction of a double quasi-Poisson bracket on the group algebra associated to the twisted fundamental group of a marked oriented surface (S, P) with boundary, where P is a finite set of marked points on the boundary of the surface S such that on every boundary component there is at least one point of P. We show that this double bracket is a noncommutative generalization of the well-known Goldman bracket, defined on the space of free homotopy classes of loops on S. For an algebra A without polynomial identities, we construct a double bracket on the space of decorated twisted \({{\,\textrm{GL}\,}}_n(A)\) GL n ( A ) -, symplectic and indefinite orthogonal local systems.