### 7.5.8 involut_lib

Library:
  involut.lib
Purpose:
  Computations and operations with involutions
Authors:
  Oleksandr Iena, yena@mathematik.uni-kl.de,
  Markus Becker, mbecker@mathematik.uni-kl.de,
  Viktor Levandovskyy, levandov@mathematik.uni-kl.de

Overview:
  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.

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

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

Procedures:

> 7.5.8.0. findInvo |  | computes linear involutions on a basering;
> 7.5.8.0. findInvoDiag |  | computes homothetic (diagonal) involutions on a basering;
> 7.5.8.0. findAuto |  | computes linear automorphisms of order n of a basering;
> 7.5.8.0. ncdetection |  | computes an ideal, presenting an involution map on some particular noncommutative algebras;
> 7.5.8.0. involution |  | applies the involution to an object;
> 7.5.8.0. isInvolution |  | check whether a map F in an involution;
> 7.5.8.0. isAntiEndo |  | check whether a map F in an antiendomorphism.

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