scholarly journals Topological algebras with an orthogonal total sequence

1997 ◽  
Vol 72 (2) ◽  
pp. 215-222 ◽  
Author(s):  
Hermann Render
Keyword(s):  
Topological Algebras ◽  
Total Sequence

TOPOLOGICAL CONFORMAL ALGEBRA IN POLYAKOV’S LIGHT-CONE GAUGE GRAVITY

1992 ◽  
Vol 07 (35) ◽  
pp. 3291-3302 ◽  
Author(s):  
KIYONORI YAMADA
Keyword(s):  
Light Cone ◽  
Matter Field ◽  
Conformal Algebra ◽  
Two Dimensional ◽  
Topological Algebras ◽  
Light Cone Gauge ◽  
Brst Cohomology ◽  
Dimensional Gravity ◽  
Conformal Gauge ◽  
Gauge Gravity

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.

scholarly journals A class of factorable topological algebras

1990 ◽  
Vol 33 (1) ◽  
pp. 53-59 ◽  
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

2014 ◽  
Vol 66 (1) ◽  
pp. 205-240 ◽  
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.

scholarly journals Subsets of nonempty joint spectrum in topological algebras

2018 ◽  
Vol 143 (4) ◽  
pp. 441-448
Author(s):  
Antoni Wawrzyńczyk
Keyword(s):  
Topological Algebras ◽  
Joint Spectrum

scholarly journals Diversity of dinoflagellate assemblages in coastal temperate and offshore tropical waters of Australia

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Tahnee Manning ◽  
Arjun Venkatesh Thilagaraj ◽  
Dmitri Mouradov ◽  
Richard Piola ◽  
Clare Grandison ◽  
...  
Keyword(s):  
Dissolved Oxygen ◽  
High Throughput ◽  
Harmful Algal Blooms ◽  
Algal Blooms ◽  
High Throughput Sequencing ◽  
Environmental Parameters ◽  
Marine Phytoplankton ◽  
Tropical Waters ◽  
Total Sequence ◽  
Phytoplankton Communities

Abstract Background Dinoflagellates are a ubiquitous and ecologically important component of marine phytoplankton communities, with particularly notable species including those associated with harmful algal blooms (HABs) and those that bioluminesce. High-throughput sequencing offers a novel approach compared to traditional microscopy for determining species assemblages and distributions of dinoflagellates, which are poorly known especially in Australian waters. Results We assessed the composition of dinoflagellate assemblages in two Australian locations: coastal temperate Port Phillip Bay and offshore tropical waters of Davies Reef (Great Barrier Reef). These locations differ in certain environmental parameters reflecting latitude as well as possible anthropogenic influences. Molecular taxonomic assessment revealed more species than traditional microscopy, and it showed statistically significant differences in dinoflagellate assemblages between locations. Bioluminescent species and known associates of HABs were present at both sites. Dinoflagellates in both areas were mainly represented by the order Gymnodiniales (66%—82% of total sequence reads). In the warm waters of Davies Reef, Gymnodiniales were equally represented by the two superclades, Gymnodiniales sensu stricto (33%) and Gyrodinium (34%). In contrast, in cooler waters of Port Phillip Bay, Gymnodiniales was mainly represented by Gyrodinium (82%). In both locations, bioluminescent dinoflagellates represented up to 0.24% of the total sequence reads, with Protoperidinium the most abundant genus. HAB-related species, mainly represented by Gyrodinium, were more abundant in Port Phillip Bay (up to 47%) than at Davies Reef (28%), potentially reflecting anthropogenic influence from highly populated and industrial areas surrounding the bay. The entire assemblage of dinoflagellates, as well as the subsets of HAB and bioluminescent species, were strongly correlated with water quality parameters (R2 = 0.56–0.92). Significant predictors differed between the subsets: HAB assemblages were explained by salinity, temperature, dissolved oxygen, and total dissolved solids; whereas, bioluminescent assemblages were explained only by salinity and dissolved oxygen, and had greater variability. Conclusion High-throughput sequencing and genotyping revealed greater diversity of dinoflagellate assemblages than previously known in both subtropical and temperate Australian waters. Significant correlations of assemblage structure with environmental variables suggest the potential for explaining the distribution and composition of both HAB species and bioluminescent species.

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