scholarly journals 4d $$ \mathcal{N} $$ = 2 SCFTs and lisse W-algebras

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Dan Xie ◽  
Wenbin Yan
Keyword(s):  
Large Class ◽  
Finite Dimensional ◽  
Associated Variety ◽  
The Relationship

Abstract We continue our studies of the correspondence between 4d $$ \mathcal{N} $$ N = 2 SCFTs and 2d W-algebras. The purpose of this paper is to study the relationship between 2d lisse W-algebras and their 4d SCFT partners. The lisse W-algebra is the W-algebra whose associated Zhu’s C2 algebra is finite dimensional. As the associated variety of Zhu’s C2 algebra is identified with the Higgs branch in the 4d/2d correspondence, the lisse condition is equivalent to the absence of the Higgs branch on the 4d side. We classify 4d $$ \mathcal{N} $$ N = 2 SCFTs which do not admit Higgs branch, then these theories would give lisse W-algebras through the 4d/2d correspondence. In particular, we predict the existence of a large class of new non-admissible lisse W-algebras, which have not been studied before. The 4d theories corresponding to lisse W-algebra can appear in the Higgs branches of generic 4d $$ \mathcal{N} $$ N = 2 SCFTs, therefore they are crucial to understand the Higgs branches of $$ \mathcal{N} $$ N = 2 SCFTs.

scholarly journals Characteristic phenomena in combustion

1997 ◽  
Vol 1 (2) ◽  
pp. 147-159
Author(s):  
Dirk Meinköhn
Keyword(s):  
State Space ◽  
Reaction Diffusion ◽  
Stationary Solutions ◽  
The State ◽  
State Variable ◽  
Finite Dimensional ◽  
Dimensional State Space ◽  
Singularity Order ◽  
The Relationship ◽  
Stable Stationary Solutions

For the case of a reaction–diffusion system, the stationary states may be represented by means of a state surface in a finite-dimensional state space. In the simplest example of a single semi-linear model equation given. in terms of a Fredholm operator, and under the assumption of a centre of symmetry, the state space is spanned by a single state variable and a number of independent control parameters, whereby the singularities in the set of stationary solutions are necessarily of the cuspoid type. Certain singularities among them represent critical states in that they form the boundaries of sheets of regular stable stationary solutions. Critical solutions provide ignition and extinction criteria, and thus are of particular physical interest. It is shown how a surface may be derived which is below the state surface at any location in state space. Its contours comprise singularities which correspond to similar singularities in the contours of the state surface, i.e., which are of the same singularity order. The relationship between corresponding singularities is in terms of lower bounds with respect to a certain distinguished control parameter associated with the name of Frank-Kamenetzkii.

scholarly journals Primal Lower Nice Functions in Reflexive Smooth Banach Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2066
Author(s):  
Messaoud Bounkhel ◽  
Mostafa Bachar
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Space Setting ◽  
Nonlinear Anal ◽  
Finite Dimensional ◽  
In Trans ◽  
First Time ◽  
The Relationship ◽  
Primal Lower Nice Functions

In the present work, we extend, to the setting of reflexive smooth Banach spaces, the class of primal lower nice functions, which was proposed, for the first time, in finite dimensional spaces in [Nonlinear Anal. 1991, 17, 385–398] and enlarged to Hilbert spaces in [Trans. Am. Math. Soc. 1995, 347, 1269–1294]. Our principal target is to extend some existing characterisations of this class to our Banach space setting and to study the relationship between this concept and the generalised V-prox-regularity of the epigraphs in the sense proposed recently by the authors in [J. Math. Anal. Appl. 2019, 475, 699–29].

scholarly journals ON REPRESENTATIONS OF QUANTUM GROUPS Uq(fm(K,H))

2008 ◽  
Vol 78 (2) ◽  
pp. 261-284 ◽  
Author(s):  
XIN TANG ◽  
YUNGE XU
Keyword(s):  
Quantum Groups ◽  
Irreducible Representations ◽  
Whittaker Model ◽  
Finite Dimensional ◽  
Completely Reducible ◽  
The Relationship ◽  
Natural Families

AbstractWe construct families of irreducible representations for a class of quantum groups Uq(fm(K,H). First, we realize these quantum groups as hyperbolic algebras. Such a realization yields natural families of irreducible weight representations for Uq(fm(K,H)). Second, we study the relationship between Uq(fm(K,H)) and Uq(fm(K)). As a result, any finite-dimensional weight representation of Uq(fm(K,H)) is proved to be completely reducible. Finally, we study the Whittaker model for the center of Uq(fm(K,H)), and a classification of all irreducible Whittaker representations of Uq(fm(K,H)) is obtained.

Federer-Čech Couples

1969 ◽  
Vol 21 ◽  
pp. 842-864
Author(s):  
Micheal Dyer
Keyword(s):  
Simplicial Complex ◽  
Large Class ◽  
Metric Space ◽  
Topological Spaces ◽  
Compact Open Topology ◽  
Finite Dimensional ◽  
Cw Complexes

In (5),I considered two-term conditions in π-exact couples, of which the exact couple of Federer (7) is an example. Let M(X, Y)be the space of all maps from X to Y with the compact-open topology. Our aim in this paper is to construct a π-exact couple , where Xis a finite-dimensional (in the sense of Lebesgue) metric space and , a certain (rather large) class of spaces. Specifically, is the class of all topological spaces Xwhich possess the following property (P).(P) Let Y be a (possibly infinite) simplicial complex. There exists x0 ∈ X and y0 ∊ Y such that [X, x0]≃ [Y, y0].In § 5 it will be seen that contains all CW complexes and all metric absolute neighbourhood retracts (ANR)s.

Cell Complexes, Valuations, and the Euler Relation

1970 ◽  
Vol 22 (2) ◽  
pp. 235-241 ◽  
Author(s):  
M. A. Perles ◽  
G. T. Sallee
Keyword(s):  
Euclidean Space ◽  
Hausdorff Metric ◽  
Dimensional Euclidean Space ◽  
Cell Complexes ◽  
Finite Dimensional ◽  
Finite Set ◽  
Euler Relation ◽  
Set Of Points ◽  
The Relationship ◽  
Dimensional Face

1. Recently a number of functions have been shown to satisfy relations on polytopes similar to the classic Euler relation. Much of this work has been done by Shephard, and an excellent summary of results of this type may be found in [11]. For such functions, only continuity (with respect to the Hausdorff metric) is required to assure that it is a valuation, and the relationship between these two concepts was explored in [8]. It is our aim in this paper to extend the results obtained there to illustrate the relationship between valuations and the Euler relation on cell complexes.To fix our notions, we will suppose that everything takes place in a given finite-dimensional Euclidean space X.A polytope is the convex hull of a finite set of points and will be referred to as a d-polytope if it has dimension d. Polytopes have faces of all dimensions from 0 to d – 1 and each of these is in turn a polytope. A k-dimensional face will be termed simply a k-face.

Ulam Games, Łukasiewicz Logic, and AF C*-Algebras

1993 ◽  
Vol 18 (2-4) ◽  
pp. 151-161
Author(s):  
Daniele Mundici
Keyword(s):  
Search Space ◽  
Error Correcting Codes ◽  
Strong Unit ◽  
C Algebras ◽  
Finite Dimensional ◽  
Minimum Number ◽  
Boolean Search ◽  
Game Theoretic ◽  
The Relationship ◽  
Mv Algebras

Ulam asked what is the minimum number of yes-no questions necessary to find an unknown number in the search space (1, …, 2n), if up to l of the answers may be erroneous. The solutions to this problem provide optimal adaptive l error correcting codes. Traditional, nonadaptive l error correcting codes correspond to the particular case when all questions are formulated before all answers. We show that answers in Ulam’s game obey the (l+2)-valued logic of Łukasiewicz. Since approximately finite-dimensional (AF) C*-algebras can be interpreted in the infinite-valued sentential calculus, we discuss the relationship between game-theoretic notions and their C*-algebraic counterparts. We describe the correspondence between continuous trace AF C*-algebras, and Ulam games with separable Boolean search space S. whose questions are the clopen subspaces of S. We also show that these games correspond to finite products of countable Post MV algebras, as well as to countable lattice-ordered Specker groups with strong unit.

Characters of nilpotent groups

1984 ◽  
Vol 96 (1) ◽  
pp. 123-137 ◽  
Author(s):  
A. L Carey ◽  
W. Moran
Keyword(s):  
Conjugacy Class ◽  
Large Class ◽  
Nilpotent Groups ◽  
Positive Definite ◽  
Primitive Ideals ◽  
Finite Conjugacy ◽  
Finite Conjugacy Class ◽  
The Relationship

AbstractThe characters (extremal positive definite central functions) of discrete nilpotent groups are studied. The relationship between the set of characters of G and the primitive ideals of the group C*-algebra C*(G) is investigated. It is shown that for a large class of nilpotent groups these objects are in 1–1 correspondence. One proof of this exploits the fact that faithful characters of certain nilpotent groups vanish off the finite conjugacy class subgroup. An example is given where the latter property fails.

Derivations in Prime Rings

1983 ◽  
Vol 26 (3) ◽  
pp. 267-270 ◽  
Author(s):  
Jeffrey Bergen
Keyword(s):  
Commutative Ring ◽  
Prime Ring ◽  
Simple Algebra ◽  
Finitely Generated ◽  
Prime Rings ◽  
Finite Dimensional ◽  
The Relationship

AbstractLet R be a prime ring and d≠0 a derivation of R. We examine the relationship between the structure of R and that of d(R). We prove that if R is an algebra over a commutative ring A such that d(R) is a finitely generated submodule then R is an order in a simple algebra finite dimensional over its center.

scholarly journals On the convergence of min/sup points in optimal control problems

2001 ◽  
Vol 6 (1) ◽  
pp. 35-52
Author(s):  
Adib Bagh
Keyword(s):  
Optimal Control ◽  
Large Class ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Finite Dimensional ◽  
Lopsided Convergence ◽  
Definition Of ◽  
Stability Results ◽  
Convex Control

We modify the definition of lopsided convergence of bivariate functionals to obtain stability results for the min/sup points of some control problems. In particular, we develop a scheme of finite dimensional approximations to a large class of non-convex control problems.

scholarly journals TILTING MUTATION FOR m-REPLICATED ALGEBRAS

2011 ◽  
Vol 10 (04) ◽  
pp. 649-664 ◽  
Author(s):  
HONGBO LV ◽  
SHUNHUA ZHANG
Keyword(s):  
Closed Field ◽  
Cluster Category ◽  
Tilting Module ◽  
Hereditary Algebra ◽  
Algebraically Closed Field ◽  
Finite Dimensional ◽  
Left Part ◽  
The Relationship

Let A be a finite-dimensional hereditary algebra over an algebraically closed field k, A(m) be the m-replicated algebra of A and [Formula: see text] be the m-cluster category of A. In this paper, we introduce the notion of mutation team in mod A(m), and prove that each faithful almost complete tilting module over A(m) has a mutation team by showing that the sequence of the complements satisfies the properties of the mutation team. We also prove that for each partial mutation team in the m-left part of mod A(m), there exists a faithful almost complete tilting module having the partial mutation team as the set of indecomposable complements. As an application, we prove that m-cluster mutation in [Formula: see text] can be realized as tilting mutation in mod A(m), and we also give the relationship between connecting sequences in mod A(m) and higher AR-angles in the m-cluster category [Formula: see text].

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