Higher Derived Brackets for Arbitrary Derivations
Higher Derived Brackets for Arbitrary Derivations
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任意导数的更高派生括号
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
T. Voronov
中科院分区：
文献类型：
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作者：
T. Voronov
引入并研究了由李超代数的导子(不一定是内导子)生成的高阶导数括号的构造。我们在早期的工作中引入了由李超代数的一个元素生成的高阶导数括号。高阶派生括号的例子自然会出现在几何和数学物理中。从一个完全不同的角度，我们证明了当人们想要将具有给定的补子代数的微分李超代数的子代数的包含映射转化为纤维时，出现了高导括号。(对于非交换补子代数，这将导致具有下降或减弱(反)括号对称性的$L_{infty}$-代数的推广。)
We introduce and study a construction of higher derived brackets generated by a (not necessarily inner) derivation of a Lie superalgebra. Higher derived brackets generated by an element of a Lie superalgebra were introduced in our earlier work. Examples of higher derived brackets naturally appear in geometry and mathematical physics. From a totally different viewpoint, we show that higher derived brackets arise when one wants to turn the inclusion map of a subalgebra of a differential Lie superalgebra, with a given complementary subalgebra, into a fibration. (For a non-Abelian complementary subalgebra, this leads to a generalization of $L_{infty}$-algebras with dropped or weakened (anti)symmetry of the brackets.)