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Triple system

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MathematicsAnalysisManifoldsNice Vector Field

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In algebra, a triple system is a vector space $V$ over a field $K$ with a ternary operation which is a $K$-trilinear mapping $V \times V \times V \rightarrow V$. They are used in the theory of non-associative algebras and appear in the construction of Lie algebras. Examples include Freudenthal–Kantor triple systems, Jordan triple systems, Lie triple systems, Anti-Lie triple systems and Allison-Hein triple systems.

In combinatorics, a triple system is a class of block design with blocks of size $3$. Examples include Steiner triple system and Kirkman triple system.

How to Cite This Entry:
Triple system. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Triple_system&oldid=42986

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Nice Vector FieldMathematics / Analysis / Manifolds / Nice Vector Fieldmethod: title_similarity - confidence: 0.90suggested

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Triple systemencyclopedia_of_mathematics

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Jordan triple systemoutgoing citation Allison-Hein triple systemoutgoing citation Multilinear mappingoutgoing citation Steiner triple systemoutgoing citation Non-associative rings and algebrasoutgoing citation Lie algebraoutgoing citation Algebraic operationoutgoing citation Lie triple systemoutgoing citation Vector spaceoutgoing citation Anti-Lie triple systemoutgoing citation Anti-Lie triple systemincoming citation Jordan triple systemincoming citation Lie triple systemincoming citation Freudenthal-Kantor triple systemincoming citation Allison-Hein triple systemincoming citation Triple productincoming citation

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subcategory_ofconcept:triple-system -> topic:nice-vector-fieldconfidence: 0.90 - provenance: title_similarity classificationsuggested

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