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Rings : jewelry of power, love and loyalty
The author considers rings in all their forms and makes their context come alive through paintings, drawings and vivid quotations.
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
New rings : 500+ designs : with over 600 illustrations
This illustrated survey showcases 591 contemporary rings that have been created by nearly 300 international designers and is divided into five sections - one for each finger.
Book
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
Men's rings
Published in conjunction with the exhibition of Yves Gastou's collection at the L'ECOLE, School of Jewelry Arts October 5-November 30, 2018.
Book
Rigid Character Groups, Lubin-Tate Theory, and (𝜑,Γ)-Modules
The construction of the $p$-adic local Langlands correspondence for $\\mathrm{GL}_2(\\mathbf{Q}_p)$ uses in an essential way Fontaine's theory of cyclotomic $(\\varphi ,\\Gamma )$-modules. Here cyclotomic means that $\\Gamma = \\mathrm {Gal}(\\mathbf{Q}_p(\\mu_{p^\\infty})/\\mathbf{Q}_p)$ is the Galois group of the cyclotomic extension of $\\mathbf Q_p$. In order to generalize the $p$-adic local Langlands correspondence to $\\mathrm{GL}_{2}(L)$, where $L$ is a finite extension of $\\mathbf{Q}_p$, it seems necessary to have at our disposal a theory of Lubin-Tate $(\\varphi ,\\Gamma )$-modules. Such a generalization has been carried out, to some extent, by working over the $p$-adic open unit disk, endowed with the action of the endomorphisms of a Lubin-Tate group. The main idea of this article is to carry out a Lubin-Tate generalization of the theory of cyclotomic $(\\varphi ,\\Gamma )$-modules in a different fashion. Instead of the $p$-adic open unit disk, the authors work over a character variety that parameterizes the locally $L$-analytic characters on $o_L$. They study $(\\varphi ,\\Gamma )$-modules in this setting and relate some of them to what was known previously.
eBook
The rings book
This practical jewellery handbook looks at the history and significance of rings and then guides the reader through a series of step-by-step projects. This edition features a new gallery at the back of the book.
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