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7.7.9 involut_lib

Computations and operations with involutions
Oleksandr Iena, yena@mathematik.uni-kl.de,
Markus Becker, mbecker@mathematik.uni-kl.de,
Viktor Levandovskyy, levandov@mathematik.uni-kl.de

Involution is an anti-automorphism of a non-commutative K-algebra with the property that applied an involution twice, one gets an identity. Involution is linear with respect to the ground field. In this library we compute linear involutions, distinguishing the case of a diagonal matrix (such involutions are called homothetic) and a general one. Also, linear automorphisms of different order can be computed.

Forschungsschwerpunkt 'Mathematik und Praxis' (Project of Dr. E. Zerz and V. Levandovskyy), Uni Kaiserslautern

This library provides algebraic tools for computations and operations with algebraic involutions and linear automorphisms of non-commutative algebras

Procedures: findInvo  computes linear involutions on a basering; findInvoDiag  computes homothetic (diagonal) involutions on a basering; findAuto  computes linear automorphisms of order n of a basering; ncdetection  computes an ideal, presenting an involution map on some particular noncommutative algebras; involution  applies the involution to an object; isInvolution  check whether a map F in an involution; isAntiEndo  check whether a map F in an antiendomorphism.