Algebraic theories of brackets and related (Co)homologies

Krasilshchik I.

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Algebraic theories of brackets and related (Co)homologies

机译：方括号和相关（同）同调的代数理论

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摘要

A general theory of the Fr?licher-Nijenhuis and Schouten-Nijenhuis brackets in the category of modules over a commutative algebra is described. Some related structures and (co)homology invariants are discussed, as well as applications to geometry.

机译：描述了交换代数上模数范畴中的Fr？licher-Nijenhuis和Schouten-Nijenhuis括号的一般理论。讨论了一些相关的结构和（共）同构不变量，以及它们在几何中的应用。

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《Acta Applicandae Mathematicae: An International Journal on Applying Mathematics and Mathematical Applications》 |2010年第1期|共14页
作者
Krasilshchik I.;
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正文语种 eng
中图分类应用数学;
关键词
Algebraic approach; Fr?licher-Nijenhuis bracket; Hamiltonian formalism; Integrability; Nonlinear differential equations; Poisson structures; Schouten-Nijenhuis bracket;

机译：代数方法;Fr？licher-Nijenhuis支架;Hamiltonian形式主义;可积性;非线性微分方程;泊松结构;Schouten-Nijenhuis支架;

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专利

1. Algebraic theories of brackets and related (Co)homologies [J] . Krasilshchik I. Acta Applicandae Mathematicae: An International Journal on Applying Mathematics and Mathematical Applications . 2010,第1期

机译：方括号和相关（同）同调的代数理论
2. Homology with trivial coefficients and universal central extensions of algebras with bracket [J] . Casas JM Communications in algebra . 2007,第8期

机译：具有平凡系数的同调性和带括号的代数的通用中心扩展
3. Graded K-theory and K-homology of relative Cuntz-Pimsner algebras and graph C*-algebras [J] . Patterson Quinn, Sierakowski Adam, Sims Aidan, Journal of Mathematical Analysis and Applications . 2021,第2期

机译：相对Cuntz-pimsner代数和图C * -algebras的渐变k理论和K-homage
4. A Homology Theory for Hybrid Systems: Hybrid Homology [C] . Aaron D. Ames, Shankar Sastry Workshop on Hybrid Systems: Computation and Control . 2005

机译：混合系统的同源性理论：杂交同源性
5. Hermitian algebraic K-theory and dihedral homology [D] . Song, Yongjin 1990

机译：埃尔米特代数K理论与二面同性
6. Higher-order syzygies for the bracket algebra and for the ring of coordinates of the Grassmanian. [O] . D Anick, G C Rota 1991

机译：括号代数和Grassmanian坐标环的高阶同构。
7. Algebraic theories of brackets and related (co)homologies [O] . Krasil'shchik, Iosif 2009

机译：括号和相关（共）同源的代数理论

Algebraic theories of brackets and related (Co)homologies

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