Singular

7.7.9 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:

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