Coequalizers and pullbacks in the category Seg of Segal topological algebras

We show that the two-dimensional gravity coupled to c=−2 matter field in Polyakov’s light-cone gauge has a twisted N=2 superconformal algebra. We also show that the BRST cohomology in the light-cone gauge actually coincides with that in the conformal gauge. Based on this observation the relations between the topological algebras are discussed.

K-theory of fine topological algebras, Chern character, and assembly

K-Theory ◽

10.1007/bf00961335 ◽

1992 ◽

Vol 6 (1) ◽

pp. 57-86 ◽

Cited By ~ 5

Author(s):

Ulrike Tillmann

Keyword(s):

Chern Character ◽

Topological Algebras ◽

K Theory

Generalized Principal Extensions in Topological Algebras

Complex Analysis and Operator Theory ◽

10.1007/s11785-011-0135-4 ◽

2011 ◽

Vol 6 (3) ◽

pp. 561-564

Author(s):

Zoi Daoultzi-Malamou

Keyword(s):

Topological Algebras

A class of factorable topological algebras

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s001309150002887x ◽

1990 ◽

Vol 33 (1) ◽

pp. 53-59 ◽

Cited By ~ 5

Author(s):

E. Ansari-Piri

Keyword(s):

Vector Space ◽

Topological Vector Space ◽

Approximate Identity ◽

Necessary Condition ◽

Topological Algebras ◽

Approximate Identities ◽

Cohen Factorization ◽

Locally Convex ◽

Space Property ◽

Uniformly Bounded

The famous Cohen factorization theorem, which says that every Banach algebra with bounded approximate identity factors, has already been generalized to locally convex algebras with what may be termed “uniformly bounded approximate identities”. Here we introduce a new notion, that of fundamentality generalizing both local boundedness and local convexity, and we show that a fundamental Fréchet algebra with uniformly bounded approximate identity factors. Fundamentality is a topological vector space property rather than an algebra property. We exhibit some non-fundamental topological vector space and give a necessary condition for Orlicz space to be fundamental.

Generalized Frobenius Algebras and Hopf Algebras

Canadian Journal of Mathematics ◽

10.4153/cjm-2012-060-7 ◽

2014 ◽

Vol 66 (1) ◽

pp. 205-240 ◽

Cited By ~ 3

Author(s):

Miodrag Cristian Iovanov

Keyword(s):

Hopf Algebras ◽

Topological Algebra ◽

Homological Algebra ◽

General Concept ◽

Frobenius Algebra ◽

Theoretic Approach ◽

Topological Algebras ◽

Infinite Dimensional ◽

Finite Case ◽

Frobenius Algebras

Abstract“Co-Frobenius” coalgebras were introduced as dualizations of Frobenius algebras. We previously showed that they admit left-right symmetric characterizations analogous to those of Frobenius algebras. We consider the more general quasi-co-Frobenius (QcF) coalgebras. The first main result in this paper is that these also admit symmetric characterizations: a coalgebra is QcF if it is weakly isomorphic to its (left, or right) rational dual Rat(C*) in the sense that certain coproduct or product powers of these objects are isomorphic. Fundamental results of Hopf algebras, such as the equivalent characterizations of Hopf algebras with nonzero integrals as left (or right) co-Frobenius, QcF, semiperfect or with nonzero rational dual, as well as the uniqueness of integrals and a short proof of the bijectivity of the antipode for such Hopf algebras all follow as a consequence of these results. This gives a purely representation theoretic approach to many of the basic fundamental results in the theory of Hopf algebras. Furthermore, we introduce a general concept of Frobenius algebra, which makes sense for infinite dimensional and for topological algebras, and specializes to the classical notion in the finite case. This will be a topological algebra A that is isomorphic to its complete topological dual Aν. We show that A is a (quasi)Frobenius algebra if and only if A is the dual C* of a (quasi)co-Frobenius coalgebra C. We give many examples of co-Frobenius coalgebras and Hopf algebras connected to category theory, homological algebra and the newer q-homological algebra, topology or graph theory, showing the importance of the concept.

Further radii in topological algebras

Bulletin of the Belgian Mathematical Society - Simon Stevin ◽

10.36045/bbms/1102715105 ◽

2002 ◽

Vol 9 (2) ◽

pp. 279-292

Author(s):

L. Oubbi

Keyword(s):

Topological Algebras

Subsets of nonempty joint spectrum in topological algebras

10.21136/mb.2018.0098-17 ◽

2018 ◽

Vol 143 (4) ◽

pp. 441-448

Author(s):

Antoni Wawrzyńczyk

Keyword(s):

Topological Algebras ◽

Joint Spectrum

Frames and topological algebras for a double-power monad

Journal of Logic and Analysis ◽

10.4115/jla.2019.11.ft5 ◽

2019 ◽

Author(s):

Giulia Frosoni ◽

Giuseppe Rosolini ◽

Alessio Santamaria

Keyword(s):

Topological Algebras