Difference between revisions of "Triple system"
From Encyclopedia of Mathematics
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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]] $V \times V \times V \rightarrow V$. Examples include [[Freudenthal–Kantor triple system]]s, [[Jordan triple system]]s, [[Lie triple system]]s, [[Anti-Lie triple system]]s and [[Allison-Hein triple system]]s. | + | 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 rings and algebras|non-associative algebras]] and appear in the construction of [[Lie algebra]]s. Examples include [[Freudenthal–Kantor triple system]]s, [[Jordan triple system]]s, [[Lie triple system]]s, [[Anti-Lie triple system]]s and [[Allison-Hein triple system]]s. |
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]]. | 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]]. | ||
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Latest revision as of 18:13, 19 March 2018
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=42980
Triple system. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Triple_system&oldid=42980