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Let $U$ be an open subset of the complex plane, and let $L$ denote a finite-dimensional complex simple Lie algebra. A. A. Belavin and V. G. Drinfel’d investigated non-degenerate meromorphic functions from $U \times U$ into $L \otimes L$ which are solutions of the classical Yang-Baxter equation [Funct. Anal. Appl. 16, 159-180 (1983; Zbl 0504.22016)]. They found that (up to equivalence) the solutions depend only on the difference of the two variables and that their set of poles forms a discrete (additive) subgroup $Γ$ of the...

Symmetric approach to the fundamental notions of general topology

Schmidt, J. (1967)

General Topology and its Relations to Modern Analysis and Algebra

Symmetrization of brace algebra

Daily, Marilyn, Lada, Tom (2006)

Proceedings of the 25th Winter School "Geometry and Physics"

Summary: We show that the symmetrization of a brace algebra structure yields the structure of a symmetric brace algebra. We also show that the symmetrization of the natural brace structure on $⨁_{k \geq 1} Hom (V^{\otimes k}, V)$ coincides with the natural symmetric brace structure on $⨁_{k \geq 1} Hom {(V^{\otimes k}, V)}^{a s}$ , the direct sum of spaces of antisymmetric maps $V^{\otimes k} \to V$ .

Symmetry: Art and Science - 2004 Sixth Interdisciplinary Symmetry Congress and Exhibition of ISIS-Symmetry

Denes Nagy, George Lugosi (2005)

Visual Mathematics

Symplectic solution supermanifolds in field theory

Schmitt, T. (1997)

Proceedings of the 16th Winter School "Geometry and Physics"

Summary: For a large class of classical field models used for realistic quantum field theoretic models, an infinite-dimensional supermanifold of classical solutions in Minkowski space can be constructed. This solution supermanifold carries a natural symplectic structure; the resulting Poisson brackets between the field strengths are the classical prototypes of the canonical (anti-) commutation relations. Moreover, we discuss symmetries and the Noether theorem in this context.

Syntopogene halbgruppen

Császár, Á. (1967)

General Topology and its Relations to Modern Analysis and Algebra

Systems of covers of frames and resulting subframes

Kříž, I., Pultr, A. (1987)

Proceedings of the 14th Winter School on Abstract Analysis

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