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 $V \times V \times V \rightarrow V$. 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
Triple system. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Triple_system&oldid=42986