Noncommutative Algebra and Applications
Projeto Temático FAPESP No.2015/091629, coordenado por César Polcino Milies
Research group seminars
2017 seminars:
Lecturer 
Title 
Date 
Time 
Room 
Francesco Matucci (IMECCUNICAMP) 
Introdução à Teoria Geométrica de Grupos (parte 2) 
November 07, 2017 
14:3015:30 
259A 
Abstract: Um grupo é uma estrutura algébrica que descreve a simetria de algum objeto. Partindo de um grupo abstrato podemos sempre associar um objeto geométrico (o grafo de Cayley) que realize esta simetria. Daremos uma breve introdução as apresentações de grupos e como no estudo deles se pode usar técnicas de outras áreas da matemática (como geometria, combinatória, ciência da computação, análise e outras). Faremos esta caminhada falando de algumas classes de grupos interessantes e propriedades deles. 
Lecturer 
Title 
Date 
Time 
Room 
Francesco Matucci (IMECCUNICAMP) 
Introdução à Teoria Geométrica de Grupos 
October 31, 2017 
14:3015:30 
259A 
Abstract: Um grupo é uma estrutura algébrica que descreve a simetria de algum objeto. Partindo de um grupo abstrato podemos sempre associar um objeto geométrico (o grafo de Cayley) que realize esta simetria. Daremos uma breve introdução as apresentações de grupos e como no estudo deles se pode usar técnicas de outras áreas da matemática (como geometria, combinatória, ciência da computação, análise e outras). Faremos esta caminhada falando de algumas classes de grupos interessantes e propriedades deles. 
Lecturer 
Title 
Date 
Time 
Room 
Jairo Z. Gonçalves (IMEUSP) 
Free subgroups in a normal subgroup of the multiplicative group of the field of fractions of k[x^{±}^{1}, y^{±}^{1}][X; σ] 
September 26, 2017 
14:3015:30 
259A 
Abstract: Let σ be an automorphism of R=k[x^{±}^{1}, y^{±}^{1}] induced by an invertible matrix A ϵ GL_{2}(\mathbb{Z}), let D be the field of fractions of the skew polynomial ring R[X; σ], and let N be a non central normal subgroup of D^{\bullet}, the multiplicative group of D. We show that N contains a free subgroup. 
Lecturer 
Title 
Date 
Time 
Room 
Misha Dokuchaev (IMEUSP) 
Globalization of partial cohomology of groups (part II) 
September 19, 2017 
14:3015:30 
259A 
Abstract: We shall discuss the relations between partial and global group cohomology. One of our main results says that given a unital partial action of a group G on a ring A, such that A is a direct product of indecomposable rings, then any partial ncocycle with values in A is globalizable. This is a joint work with Mykola Khrypchenko and Juan Jacobo Simon. 
Lecturer 
Title 
Date 
Time 
Room 
Misha Dokuchaev (IMEUSP) 
Globalization of partial cohomology of groups 
September 12 , 2017 
14:3015:30 
259A 
Abstract: We shall discuss the relations between partial and global group cohomology. One of our main results says that given a unital partial action of a group G on a ring A, such that A is a direct product of indecomposable rings, then any partial ncocycle with values in A is globalizable. This is a joint work with Mykola Khrypchenko and Juan Jacobo Simon. 
Lecturer 
Title 
Date 
Time 
Room 
Doryan Temmerman (Vrije Universiteit Brussel, Belgium) 
Bovdi units and free products in integral group rings of finite groups 
August 22, 2017 
14:3015:30 
243A 
Abstract: In
the study of the Isomorphism Problem and the Zassenhaus
Conjecture, one often seeks specific subgroups of the unit group
of an integral group ring. 
Lecturer 
Title 
Date 
Time 
Room 
Jairo Z. Gonçalves (IMEUSP) 
Free subgroups in the field of fractions of k[x,y][t;\sigma] 
June 27, 2017 
14:3015:30 
259A 
Abstract: Let k be a field, and let \sigma be a kautomorphism of the polynomial ring k[x,y] in the commuting indeterminates x and y over k. Let D be the field of fractions of the skew polynomial ring k[x,y][t;\sigma], and let D^{\bullet} be its multiplicative group. In support to Lichtman's Conjecture, we show that D^{\bullet} contains a free noncyclic subgroup. 
Lecturer 
Title 
Date 
Time 
Room 
Makar Plakhotnyk (IMEUSP) 
Max nondecomposable exponent matrices (part II) 
June 6, 2017 
14:3015:30 
243A 
Abstract: We continue our study of nonnegative exponent matrices, i.e. nonnegative matrices A = (\alpha_{pq}) with zero diagonal and such that the inequalities \alpha_{ij} +\alpha_{jk} \geq \alpha_{ik} hold for all i, j, k. We describe all exponent matrices which can not be expressed as an entrywise maximum of two noncomparable nonzero exponent matrices. This result easily implies an alternative proof of the earlier obtained description of the generators of maxplus algebra of nonnegative exponent matrices. This is a joint work with M. Dokuchaev, V. Kirichenko and G. Kudryavtseva. 
Lecturer 
Title 
Date 
Time 
Room 
Makar Plakhotnyk (IMEUSP) 
Max nondecomposable exponent matrices 
May 30, 2017 
14:3015:30 
243A 
Abstract: We continue our study of nonnegative exponent matrices, i.e. nonnegative matrices A = (\alpha_{pq}) with zero diagonal and such that the inequalities \alpha_{ij} +\alpha_{jk} \geq \alpha_{ik} hold for all i, j, k. We describe all exponent matrices which can not be expressed as an entrywise maximum of two noncomparable nonzero exponent matrices. This result easily implies an alternative proof of the earlier obtained description of the generators of maxplus algebra of nonnegative exponent matrices. This is a joint work with M. Dokuchaev, V. Kirichenko and G. Kudryavtseva. 
Lecturer 
Title 
Date 
Time 
Room 
Misha Dokuchaev (IMEUSP) 
The
ideal structure of skew group rings coming from 
May 16, 2017 
14:3015:30 
243A 
Abstract:
Given
a Hausdorff, locally compact, totally disconnected topological
space X and a field K, denote by L_c(X) the algebra of all
locally constant, compactly supported functions on X, taking
values in K. For a topological partial action of a discrete group
G on X with clopen domains, we consider the corresponding partial
action of G on the algebra L_c(X) and study the ideal structure
of the partial skew group ring L_c(X) \rtimes G. We develop a
theory of induced ideals 
Lecturer 
Title 
Date 
Time 
Room 
Misha Dokuchaev (IMEUSP) 
The
ideal structure of skew group rings coming from 
May 09, 2017 
14:3015:30 
243A 
Abstract:
Given
a Hausdorff, locally compact, totally disconnected topological
space X and a field K, denote by L_c(X) the algebra of all
locally constant, compactly supported functions on X, taking
values in K. For a topological partial action of a discrete group
G on X with clopen domains, we consider the corresponding partial
action of G on the algebra L_c(X) and study the ideal structure
of the partial skew group ring L_c(X) \rtimes G. We develop a
theory of induced ideals 
Lecturer 
Title 
Date 
Time 
Room 
Misha Dokuchaev (IMEUSP) 
The
ideal structure of skew group rings coming from 
May 02, 2017 
14:3015:30 
243A 
Abstract:
Given
a Hausdorff, locally compact, totally disconnected topological
space X and a field K, denote by L_c(X) the algebra of all
locally constant, compactly supported functions on X, taking
values in K. For a topological partial action of a discrete group
G on X with clopen domains, we consider the corresponding partial
action of G on the algebra L_c(X) and study the ideal structure
of the partial skew group ring L_c(X) \rtimes G. We develop a
theory of induced ideals 
Lecturer 
Title 
Date 
Time 
Room 
Antonio Giambruno (Universita di Palermo, Italy) 
Central polynomials versus polynomial identities 
April 07, 2017 
14:3015:30 
241A 
Abstract: A central polynomial for an algebra A is a polynomial in noncommuting variables taking central values under all evaluations in A. Polynomial identities are central polynomials taking only the zero value. A central polynomial is proper if it takes at least one nonzero value. The existence of proper central polynomials for n x n matrices was conjectured by Kaplansky in the 50's and proved in the early 70's independently by Formanek and Razmyslov. Here we want to compare the growth of the space of central polynomials to the growth of the space of polynomial identities for any finite dimensional algebra in characteristic zero. 
Lecturer 
Title 
Date 
Ti 

Jairo Z. Gonçalves (IMEUSP) 
Free
symmetric and unitary pairs in the field of 
March 28, 2017 
14:3015:30 
243A 
Abstract: Let G be a free nilpotent group, let kG be the group algebra of G over the field k of characteristic different from 2, let D be its field of fractions, and let D^{\bullet} be the multiplicative group of D. If * is an involution of G extended linearly to kG, and to D, then D^{\bullet} contains free pairs of *symmetric and *unitary elements. If N is a normal subgroup of D^{\bullet} which contains G, and such that N*=N, then N contains free symmetric pairs. Some partial results are presented when char k=2. 
Lecturer 
Title 
Date 
Time 
Room 
Jairo Gonçalves (IMEUSP) 
Free
symmetric and unitary pairs in the field of 
March 21, 2017 
14:3015:30 
243A 
Abstract: Let G be a free nilpotent group, let kG be the group algebra of G over the field k of characteristic different from 2, let D be its field of fractions, and let D^{\bullet} be the multiplicative group of D. If * is an involution of G extended linearly to kG, and to D, then D^{\bullet} contains free pairs of *symmetric and *unitary elements. If N is a normal subgroup of D^{\bullet} which contains G, and such that N*=N, then N contains free symmetric pairs. Some partial results are presented when char k=2. 