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M. Kontsevich’s graph complex and the Grothendieck–Teichmüller Lie algebra
, 2010We show that the zeroth cohomology of M. Kontsevich’s graph complex is isomorphic to the Grothendieck–Teichmüller Lie algebra $$\mathfrak {{grt}}_1$$grt1. The map is explicitly described. This result has applications to deformation quantization and Duflo
T. Willwacher
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Algebra, Lie Group and Lie Algebra
2010Geometry, algebra, and analysis are usually called the three main branches of mathematics. This chapter introduces some fundamental results in algebra that are mostly useful in systems and control. In section 4.1 some basic concepts of group and three homomorphism theorems are discussed. Ring and algebra are introduced briefly in section 4.2. As a tool,
Daizhan Cheng, Tielong Shen, Xiaoming Hu
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The Lie algebra of derivations of a current Lie algebra
Communications in Algebra, 2019Let K be a field of characteristic zero, g be a finite dimensional K-Lie algebra and let A be a finite dimensional associative and commutative K-algebra with unit.
Ochoa Arango, Jesús Alonso +1 more
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Siberian Mathematical Journal, 1992
An algebra in which any two elements generate a Lie subalgebra is called binary-Lie. Over a field of characteristic \(\neq 2\), such algebras are defined by the identities \(x^ 2=0\) and \(((xy)y)x+((yx)x)y=0\). An algebra is called algebraic if every right multiplication operator satisfies a polynomial equation; and if the degrees of these equations ...
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An algebra in which any two elements generate a Lie subalgebra is called binary-Lie. Over a field of characteristic \(\neq 2\), such algebras are defined by the identities \(x^ 2=0\) and \(((xy)y)x+((yx)x)y=0\). An algebra is called algebraic if every right multiplication operator satisfies a polynomial equation; and if the degrees of these equations ...
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Nilpotent Lie Algebras and Solvable Lie Algebras
1987The Lie algebras considered in this chapter are finite-dimensional algebras over a field k. In Sees. 7 and 8 we assume that k has characteristic 0. The Lie bracket of x and y is denoted by [x, y], and the map y → [x, y] by ad x.
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Lie Algebras, Lie Groups, and Algebra of Incidence
2018We have learned that readers of the work of D. Hestenes and G. Sobzyk (Hestenes and Sobczyk (1984). Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics.) [138] Chap. 8 and a late article of Ch. Doran, D. Hestenes and F. Sommen (Doran, Hestenes, Sommen and Van Acker (1993).
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Biderivations and linear commuting maps on the Lie algebra
, 2017Xiao Cheng +3 more
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Variational algorithms for linear algebra
Science Bulletin, 2021Xiaosi Xu, Jinzhao Sun, Suguru Endo
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Lie Algebra Cohomology and the Generalized Borel-Weil Theorem
, 1961B. Kostant
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