scholarly journals Multiplicative structures and the twisted Baum-Connes assembly map

2017 ◽  
Vol 369 (7) ◽  
pp. 5241-5269 ◽  
Author(s):  
Noé Bárcenas ◽  
Paulo Carrillo Rouse ◽  
Mario Velásquez
Keyword(s):  
Assembly Map ◽  
Multiplicative Structures

scholarly journals On the K-theory of the loop space of a Lie group

1974 ◽  
Vol 76 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Francis Clarke
Keyword(s):  
Lie Group ◽  
Loop Space ◽  
Simple Structure ◽  
Homology Theory ◽  
Compact Lie Group ◽  
Classifying Space ◽  
K Theory ◽  
Simply Connected ◽  
Torsion Free ◽  
Multiplicative Structures

Let G be a simply connected, semi-simple, compact Lie group, let K* denote Z/2-graded, representable K-theory, and K* the corresponding homology theory. The K-theory of G and of its classifying space BG are well known, (8),(1). In contrast with ordinary cohomology, K*(G) and K*(BG) are torsion-free and have simple multiplicative structures. If ΩG denotes the space of loops on G, it seems natural to conjecture that K*(ΩG) should have, in some sense, a more simple structure than H*(ΩG).

Hochschild cohomology of m-cluster tilted algebras of type 𝔸̃

2020 ◽  
pp. 2150018
Author(s):  
Viviana Gubitosi
Keyword(s):  
Hochschild Cohomology ◽  
Cohomology Groups ◽  
Tilted Algebra ◽  
Type Formula ◽  
Tilted Algebras ◽  
Gerstenhaber Algebra ◽  
Cluster Tilted Algebra ◽  
Multiplicative Structures

In this paper, we compute the dimension of the Hochschild cohomology groups of any [Formula: see text]-cluster tilted algebra of type [Formula: see text]. Moreover, we give conditions on the bounded quiver of an [Formula: see text]-cluster tilted algebra [Formula: see text] of type [Formula: see text] such that the Gerstenhaber algebra [Formula: see text] has nontrivial multiplicative structures. We also show that the derived class of gentle [Formula: see text]-cluster tilted algebras is not always completely determined by the dimension of the Hochschild cohomology.

GRASSMANNIAN SEMIGROUPS AND THEIR REPRESENTATIONS

2018 ◽  
Vol 104 (3) ◽  
pp. 308-337
Author(s):  
VICTOR CAMILLO ◽  
MIODRAG C. IOVANOV
Keyword(s):  
Representation Theory ◽  
Partial Order ◽  
Finite Semigroup ◽  
Arbitrary Field ◽  
Young Diagrams ◽  
Internal Properties ◽  
Reduced Matrices ◽  
Multiplicative Structures

The set of row reduced matrices (and of echelon form matrices) is closed under multiplication. We show that any system of representatives for the $\text{Gl}_{n}(\mathbb{K})$ action on the $n\times n$ matrices, which is closed under multiplication, is necessarily conjugate to one that is in simultaneous echelon form. We call such closed representative systems Grassmannian semigroups. We study internal properties of such Grassmannian semigroups and show that they are algebraic semigroups and admit gradings by the finite semigroup of partial order preserving permutations, with components that are naturally in one–one correspondence with the Schubert cells of the total Grassmannian. We show that there are infinitely many isomorphism types of such semigroups in general, and two such semigroups are isomorphic exactly when they are semiconjugate in $M_{n}(\mathbb{K})$. We also investigate their representation theory over an arbitrary field, and other connections with multiplicative structures on Grassmannians and Young diagrams.

scholarly journals DUALIZING THE COARSE ASSEMBLY MAP

2005 ◽  
Vol 5 (02) ◽  
pp. 161 ◽  
Author(s):  
Heath Emerson ◽  
Ralf Meyer
Keyword(s):  
Assembly Map

Formação de Professor e as Estruturas Multiplicativas: em Busca de Elementos Potencializadores da Aprendizagem Docente

2017 ◽  
Vol 10 (2) ◽  
pp. 107
Author(s):  
Aparecido dos Santos
Keyword(s):  
Teacher Learning ◽  
Teaching And Learning ◽  
Teaching Practice ◽  
Sao Paulo ◽  
Theory And Practice ◽  
São Paulo ◽  
Teacher Student ◽  
Student Relationship ◽  
Process Elements ◽  
Multiplicative Structures

O objetivo do presente estudo é o de identificar possíveis indícios de aprendizagem docente em um processo formativo com dimensões colaborativas. O processo de formação se pautou em dois pilares: na reflexão sobre o ensino e aprendizagem das estruturas multiplicativas e nas estratégias formativas empreendidas para o seu desenvolvimento (ação-reflexão-ação) a partir da análise da prática docente. O estudo foi realizado com um grupo de 14 professoras, atuantes nos anos iniciais do Ensino Fundamental, de uma escola pública na cidade de São Paulo. Os resultados apontam que, para além, da ação e reflexão sobre a prática, que permitiu proceder análises conceituais, didáticas e cognitivas que, em última análise, qualificaram o repertório teórico-prático para o ensino das estruturas multiplicativas, foi possível identificar nos relatos descritos pelas participantes, na avaliação final do processo formativo, elementos que, a meu ver, foram potencilizadores e indicaram indícios da aprendizagem docente. Essa aprendizagem, na voz das professoras, se deu na interface de quatro dimensões: (a) na relação professor- aluno, (b) na relação professor-professor- formadores, (c) na relação teoria e prática, e (d) na reflexão sobre a prática pedagógica.Palavras-chave: Processo Formativo. Aprendizagem Docente. Reflexão. Prática. AbstractThe objective of the present study is to identify possible evidence of teacher learning in a formative process with collaborative dimensions. The formation process was based on two pillars: reflection on the teaching and learning of multiplicative structures and the formative strategies undertaken for its development (action-reflection-action) from the analysis of teaching practice. The study was performed with a group of 14 teachers, active in the initial years of Elementary School, of a public school in the city of São Paulo. The results show that, in addition to the action and reflection on the practice, which allowed us to proceed with conceptual, didactic and cognitive analyzes that ultimately qualified the theoretical-practical repertoire for the teaching of multiplicative structures, it was possible to identify in the described narratives by the participants, in the final evaluation of the formative process, elements that, in my view, were definitive and indicated indications of teacher learning. This learning, in the teachers’ voice, took place in the four-dimensional interface: (a) in the teacher-student relationship, (b) in the teacher-teacher-formers relationship, (c) in the relation theory and practice, and (d) reflection on pedagogical practice.Keywords: Formative Process. Teacher Learning. Reflection. Practice

scholarly journals KK-Theory of C*-Categories and the Analytic Assembly Map

K-Theory ◽  
2002 ◽  
Vol 26 (4) ◽  
pp. 307-344 ◽  
Author(s):  
Paul D. Mitchener
Keyword(s):  
Assembly Map
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