2 research outputs found
Partially commutative and differential graded algebraic structures
PhD ThesisThe objects of study in this thesis are partially commutative and di erential
graded algebraic structures. In fact my thesis is in two parts. The rst on partially
commutative algebraic structures is concerned with automorphism groups of par-
tially commutative groups and their nite presentations. The second on di erential
graded algebraic structures is concerned with di erential graded modules.
I have given a description for Aut(G ), the automorphism group of the partially
commutative group G following Day's work, where is a nite simple graph.
I have given a description for the subgroup Conj(G ) of automorphism group
Aut(G ) following Toinet's work.
We have found a nite presentation for the subgroup ConjV of the automorphism
group Aut(G ).
I have developed AutParCommGrp (Finite Presentations of Automor-
phism Groups of Partially Commutative Groups and Their Subgroups) a
package using the GAP system for computation of a nite presentation for Aut(G ),
Conj(G ) and ConjV respectively.
In the second part of the thesis we consider the following situation: Let K be
a eld of characteristic two and let R = K[x1; x2; ; xn] be a graded polynomial
ring, graded in the negative way. Suppose M is a di erential graded R-module
with di erential @ of degree P. We have constructed a classi cation for some types
of di erential graded R-module where P 2, n > 1. This classi cation gives a
partial algorithm to test whether such modules are solvable. For modules outside
the classi cation we cannot decide, using our methods, whether or not they are
solvable. Also, we have proved in one case that M is solvable when R is a graded
polynomial ring, graded in the usual way (non-negatively graded) with (P 2, n >
1). We have developed an algorithm and written a GAP package SDGM (Solvable
Di erential Graded Modules) to check whether the di erential graded R-module
M with di erential @ of degree P is solvable or not. Documentation has been written
for all the packages above
A presentation for the subgroup of compressed conjugating automorphisms of a partially commutative group
‎Let be a partially commutative group‎. ‎We find a finite presentation for the subgroup of compressed‎ ‎vertex conjugating automorphisms of the automorphism group‎ ‎ of ‎. ‎We have written GAP packages which compute presentations for and its subgroups‎ ‎ and ‎