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"Representations"
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Social myths and collective imaginaries
\"Western or Eastern, ancient or modern, religious or scientific, myths are strikingly underestimated forces in contemporary society. In our rational, enlightened and supposedly civilized society myths have come to be perceived as the exclusive attribute of so-called pre-modern societies. In Social Myths and Collective Imaginaries, Gérard Bouchard conceptualizes myths as vessels of sacred values that transcend the division between primitive and modern. These vessels become so influential as to make an indelible impression on people's minds. We may no longer speak of Aphrodite or Gilgamesh but freedom, equality, social justice, environmentalism, democracy and nationalism are sacred values in our world. Nobody would deny that equality for all citizens in France, the right to property in the United States, or racial equality in South Africa are sacrosanct. Bouchard's refreshing and startling analysis reveals that as a sociological mechanism, myths have the power to bring societies together as well as tear themapart. In his own way, Bouchard awakens us to the transcendent power of myth that affects our daily lives, frequently unbeknownst to us.\"-- Provided by publisher.
Book
Cell complexes, poset topology and the representation theory of algebras arising in algebraic combinatorics and discrete geometry
In recent years it has been noted that a number of combinatorial structures such as real and complex hyperplane arrangements,
interval greedoids, matroids and oriented matroids have the structure of a finite monoid called a left regular band. Random walks on the
monoid model a number of interesting Markov chains such as the Tsetlin library and riffle shuffle. The representation theory of left
regular bands then comes into play and has had a major influence on both the combinatorics and the probability theory associated to such
structures. In a recent paper, the authors established a close connection between algebraic and combinatorial invariants of a left
regular band by showing that certain homological invariants of the algebra of a left regular band coincide with the cohomology of order
complexes of posets naturally associated to the left regular band.
The purpose of the present monograph is to further develop and
deepen the connection between left regular bands and poset topology. This allows us to compute finite projective resolutions of all
simple modules of unital left regular band algebras over fields and much more. In the process, we are led to define the class of CW left
regular bands as the class of left regular bands whose associated posets are the face posets of regular CW complexes. Most of the
examples that have arisen in the literature belong to this class. A new and important class of examples is a left regular band structure
on the face poset of a CAT(0) cube complex. Also, the recently introduced notion of a COM (complex of oriented matroids or conditional
oriented matroid) fits nicely into our setting and includes CAT(0) cube complexes and certain more general CAT(0) zonotopal complexes. A
fairly complete picture of the representation theory for CW left regular bands is obtained.
eBook
The Cambridge handbook of social representations
This handbook provides the theoretical and methodological tools for adopting a social representations approach in field research. Scholars, researchers and students in the social sciences will find it an invaluable resource for understanding contemporary social psychological concerns such as the development of identities, communities and narratives.
Book
The Representation Theory of the Increasing Monoid
We study the representation theory of the increasing monoid. Our results provide a fairly comprehensive picture of the representation
category: for example, we describe the Grothendieck group (including the effective cone), classify injective objects, establish
properties of injective and projective resolutions, construct a derived auto-duality, and so on. Our work is motivated by numerous
connections of this theory to other areas, such as representation stability, commutative algebra, simplicial theory, and shuffle
algebras.
eBook
Representation Theory of Geigle-Lenzing Complete Intersections
Weighted projective lines, introduced by Geigle and Lenzing in 1987, are important objects in representation theory. They have
tilting bundles, whose endomorphism algebras are the canonical algebras introduced by Ringel. The aim of this paper is to study their
higher dimensional analogs. First, we introduce a certain class of commutative Gorenstein rings
eBook
The dialogical mind : common sense and ethics
\"Common Sense and Ethics Dialogue has become a central theoretical concept in human and social sciences as well as in professions such as education, health, and psychotherapy. This 'dialogical turn' emphasizes the importance of social relations and interaction to our behaviour and how we make sense of the world; hence the Dialogical Mind is the mind in interaction with others - with individuals, groups, institutions, and cultures in historical perspectives. Through a combination of rigorous theoretical work and empirical investigation, Markova presents an ethics of dialogicality as an alternative to the narrow perspective of individualism and cognitivism that has traditionally dominated the field of social psychology\"-- Provided by publisher.
Book
A MINIMAL CONGRUENCE LATTICE REPRESENTATION FOR
Let
$p$
be an odd prime. The unary algebra consisting of the dihedral group of order
$2p$
, acting on itself by left translation, is a minimal congruence lattice representation of
$\\mathbb{M}_{p+1}$
.
Journal Article