scholarly journals A Hennings type invariant of 3-manifolds from a topological Hopf superalgebra

2020 ◽  
Vol 11 (4) ◽  
pp. 609-655
Author(s):  
Ngoc Phu Ha
Keyword(s):  
Hopf Superalgebra ◽  
Type Invariant

scholarly journals On types of matrices and centralizers of matrices and permutations

2014 ◽  
Vol 17 (5) ◽  
Author(s):  
John R. Britnell ◽  
Mark Wildon
Keyword(s):  
Finite Field ◽  
Alternating Groups ◽  
Type Invariant ◽  
The Matrix ◽  
Generalized Type

AbstractIt is known that the centralizer of a matrix over a finite field depends, up to conjugacy, only on the type of the matrix, in the sense defined by J. A. Green. In this paper an analogue of the type invariant is defined that in general captures more information; using this invariant the result on centralizers is extended to arbitrary fields. The converse is also proved: thus two matrices have conjugate centralizers if and only if they have the same generalized type. The paper ends with the analogous results for symmetric and alternating groups.

scholarly journals AN INVARIANT FOR SINGULAR KNOTS

2009 ◽  
Vol 18 (06) ◽  
pp. 825-840 ◽  
Author(s):  
J. JUYUMAYA ◽  
S. LAMBROPOULOU
Keyword(s):  
Hecke Algebras ◽  
Quadratic Relation ◽  
Link Invariant ◽  
Topological Interpretation ◽  
Type Invariant ◽  
Singular Link ◽  
Markov Trace ◽  
Skein Relation ◽  
Singular Knots

In this paper we introduce a Jones-type invariant for singular knots, using a Markov trace on the Yokonuma–Hecke algebras Y d,n(u) and the theory of singular braids. The Yokonuma–Hecke algebras have a natural topological interpretation in the context of framed knots. Yet, we show that there is a homomorphism of the singular braid monoid SBn into the algebra Y d,n(u). Surprisingly, the trace does not normalize directly to yield a singular link invariant, so a condition must be imposed on the trace variables. Assuming this condition, the invariant satisfies a skein relation involving singular crossings, which arises from a quadratic relation in the algebra Y d,n(u).

scholarly journals A splicing formula for the LMO invariant

2020 ◽  
pp. 1-28
Author(s):  
Gwénaël Massuyeau ◽  
Delphine Moussard
Keyword(s):  
Finite Type ◽  
Rational Homology ◽  
Three Sphere ◽  
Type Invariant ◽  
Low Degrees ◽  
Surgery Formula

Abstract We prove a “splicing formula” for the LMO invariant, which is the universal finite-type invariant of rational homology three-spheres. Specifically, if a rational homology three-sphere M is obtained by gluing the exteriors of two framed knots $K_1 \subset M_1$ and $K_2\subset M_2$ in rational homology three-spheres, our formula expresses the LMO invariant of M in terms of the Kontsevich–LMO invariants of $(M_1,K_1)$ and $(M_2,K_2)$ . The proof uses the techniques that Bar-Natan and Lawrence developed to obtain a rational surgery formula for the LMO invariant. In low degrees, we recover Fujita’s formula for the Casson–Walker invariant, and we observe that the second term of the Ohtsuki series is not additive under “standard” splicing. The splicing formula also works when each $M_i$ comes with a link $L_i$ in addition to the knot $K_i$ , hence we get a “satellite formula” for the Kontsevich–LMO invariant.

Two-parameter Quantum Superalgebras and PBW Theorem

2016 ◽  
Vol 23 (02) ◽  
pp. 303-324 ◽  
Author(s):  
Chunrui Ai ◽  
Shilin Yang
Keyword(s):  
Quantum Algebras ◽  
Hopf Superalgebra ◽  
Pbw Basis ◽  
Pbw Theorem ◽  
Two Parameter ◽  
Quantum Superalgebras

A class of two-parameter quantum algebras [Formula: see text] is constructed. It is shown that [Formula: see text] is a Hopf superalgebra. Then the PBW basis of [Formula: see text] is described. For this purpose, some commutative relations of root vectors of [Formula: see text] are given.

Quasi-Hopf Superalgebra

2004 ◽  
pp. 331-331
Author(s):  
Jian-zu Zhang ◽  
Roberto Floreanini ◽  
Steven Duplij ◽  
Steven Duplij ◽  
Dmitri Gitman ◽  
...  
Keyword(s):  
Hopf Superalgebra
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