scholarly journals Generators and relations for special linear algebras and groups

1985 ◽  
Vol 94 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Masaharu Kaneda
Keyword(s):  
Special Linear ◽  
Generators And Relations

scholarly journals THE UNIT MAP OF THE ALGEBRAIC SPECIAL LINEAR COBORDISM SPECTRUM

2019 ◽  
pp. 1-26
Author(s):  
Maria Yakerson
Keyword(s):  
Explicit Description ◽  
Homotopy Groups ◽  
Joint Work ◽  
Loop Spaces ◽  
Special Linear ◽  
Generators And Relations ◽  
Thom Spectra

In the joint work with Elmanto, Hoyois, Khan and Sosnilo, we computed infinite $\mathbb{P}^{1}$ -loop spaces of motivic Thom spectra using the technique of framed correspondences. This result allows us to express non-negative $\mathbb{G}_{m}$ -homotopy groups of motivic Thom spectra in terms of geometric generators and relations. Using this explicit description, we show that the unit map of the algebraic special linear cobordism spectrum induces an isomorphism on $\mathbb{G}_{m}$ -homotopy sheaves.

scholarly journals Irreducible modules with highest weight vectors over modular Witt and special Lie superalgebras

2019 ◽  
Vol 17 (1) ◽  
pp. 1381-1391
Author(s):  
Keli Zheng ◽  
Yongzheng Zhang
Keyword(s):  
Lie Superalgebras ◽  
Arbitrary Field ◽  
Special Linear ◽  
Highest Weight ◽  
Irreducible Modules

Abstract Let 𝔽 be an arbitrary field of characteristic p > 2. In this paper we study irreducible modules with highest weight vectors over Witt and special Lie superalgebras of 𝔽. The same irreducible modules of general and special linear Lie superalgebras, which are the 0-th part of Witt and special Lie superalgebras in certain ℤ-grading, are also considered. Then we establish a certain connection called a P-expansion between these modules.

scholarly journals Quiver origami: discrete gauging and folding

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Antoine Bourget ◽  
Amihay Hanany ◽  
Dominik Miketa
Keyword(s):  
Gauge Theories ◽  
Generators And Relations

Abstract We study two types of discrete operations on Coulomb branches of 3d$$ \mathcal{N} $$ N = 4 quiver gauge theories using both abelianisation and the monopole formula. We generalise previous work on discrete quotients of Coulomb branches and introduce novel wreathed quiver theories. We further study quiver folding which produces Coulomb branches of non-simply laced quivers. Our methods explicitly describe Coulomb branches in terms of generators and relations including mass deformations.

scholarly journals REGULAR FUNCTIONS ON THE SHILOV BOUNDARY

2005 ◽  
Vol 04 (06) ◽  
pp. 613-629 ◽  
Author(s):  
OLGA BERSHTEIN
Keyword(s):  
Symmetric Domain ◽  
Principal Series ◽  
Bounded Symmetric Domain ◽  
Bounded Symmetric Domains ◽  
Shilov Boundary ◽  
Generators And Relations ◽  
Regular Functions ◽  
Degenerate Principal Series

In this paper a *-algebra of regular functions on the Shilov boundary S(𝔻) of bounded symmetric domain 𝔻 is constructed. The algebras of regular functions on S(𝔻) are described in terms of generators and relations for two particular series of bounded symmetric domains. Also, the degenerate principal series of quantum Harish–Chandra modules related to S(𝔻) = Un is investigated.

On multiplicative systems defined by generators and relations

1953 ◽  
Vol 49 (4) ◽  
pp. 579-589 ◽  
Author(s):  
Trevor Evans
Keyword(s):  
Automorphism Group ◽  
Finite Number ◽  
Cyclic Group ◽  
Complete Information ◽  
Isomorphism Problem ◽  
Infinite Cyclic Group ◽  
Generators And Relations ◽  
Decision Method ◽  
Multiplicative Systems ◽  
Finitely Related

The techniques developed in (9) are used here to study the properties of multiplicative systems generated by one element (monogenie systems). The results are of two kinds. First, we obtain fairly complete information about the automorphisms and endo-morphisms of free and finitely related loops. The automorphism group of the free monogenie loop is the infinite cyclic group, each automorphism being obtained by mapping the generator on one of its repeated inverses. A monogenie loop with a finite, non-empty set of relations has only a finite number of endomorphisms. These are obtained by mapping the generator on some of the components, or their repeated inverses, occurring in the relations. We use the same methods to solve the isomorphism problem for monogenie loops, i.e. we give a method for determining whether two finitely related monogenie loops are isomorphic. The decision method consists essentially of constructing all homomorphisms between two given finitely related monogenie loops.

(ANTI)COMMUTATIVITY OF THE HARMONIC CREATION AND ANNIHILATION OPERATORS

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1808-1818
Author(s):  
S. KUWATA ◽  
A. MARUMOTO
Keyword(s):  
Irreducible Representation ◽  
Harmonic Oscillator ◽  
Linear Algebra ◽  
Commutation Relation ◽  
Complex Number ◽  
Single Mode ◽  
Equation Of Motion ◽  
Sufficient Condition ◽  
Special Linear ◽  
Creation And Annihilation Operators

It is known that para-particles, together with fermions and bosons, of a single mode can be described as an irreducible representation of the Lie (super) algebra 𝔰𝔩2(ℂ) (2-dimensional special linear algebra over the complex number ℂ), that is, they satisfy the equation of motion of a harmonic oscillator. Under the equation of motion of a harmonic oscillator, we obtain the set of the commutation relations which is isomorphic to the irreducible representation, to find that the equation of motion, conversely, can be derived from the commutation relation only for the case of either fermion or boson. If Nature admits of the existence of such a sufficient condition for the equation of motion of a harmonic oscillator, no para-particle can be allowed.

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