spectral parameter dependent approach to quantized algebra its multiparameter deformations and their q oscillator realizations yang baxterization of faddeev reshetikhin takhtajan algebra 1989 leading to quantum ybe is considered for a class of r matrices which satisfy hecke relations the authors apply such construction of the gl n case together with its multiparameter deformations revealing the connection between frt relations and the extended trigonometric sklyanin algebra new realizations of frt algebra through q oscillator modes are presented and their potential importance in the context of quantum integrable models is discussed a multiparametrized r matrix with the inclusion of spectral parameter is constructed as a by product

time dependent fiber bundles with local load sharing fiber bundle models where fibers have random lifetimes depending on their load histories are useful tools in explaining time dependent failure in heterogeneous materials such models shed light on diverse phenomena such as fatigue in structural materials and earthquakes in geophysical settings various asymptotic and approximate theories have been developed for bundles with various geometries and fiber load sharing mechanisms but numerical verification has been hampered by severe computational demands in larger bundles to gain insight at large size scales interest has returned to idealized fiber bundle models in 1d such simplified models typically assume either equal load sharing els among survivors or local load sharing lls where a failed fiber redistributes its load onto its two nearest flanking survivors such models can often be solved exactly or asymptotically in increasing bundle size n yet still capture the essence of failure in real materials the present work focuses on 1d bundles under lls as in previous works a fiber has failure rate following a power law in its load level with breakdown exponent ensuremath rho surviving fibers under fixed loads have remaining lifetimes that are independent and exponentially distributed we develop both new asymptotic theories and new computational algorithms that greatly increase the bundle sizes that can be treated in large replications e g one million fibers in thousands of realizations in particular we develop an algorithm that adapts several concepts and methods that are well known among computer scientists but relatively unknown among physicists to dramatically increase the computational speed with no attendant loss of accuracy we consider various regimes of ensuremath rho that yield drastically different behavior as n increases for 1 2l ensuremath rho l 1 els and lls have remarkably similar behavior they have identical lifetime distributions at ensuremath rho 1 with approximate gaussian bundle lifetime statistics and a finite limiting mean for ensuremath rho g1 this gaussian behavior also applies to els whereas lls behavior diverges sharply showing brittle weakest volume behavior in terms of characteristic elements derived from critical cluster formation for 0l ensuremath rho l1 2 els and lls again behave similarly but the bundle lifetimes are dominated by a few long lived fibers and show characteristics of strongest link extreme value distributions which apply exactly to ensuremath rho 0

unusual solutions to the yang baxter equation the complete list of non symmetric eight vertex constant solutions to the yang baxter equation is obtained and new solutions dependent on more than one variable are presented the corresponding spin hamiltonians are derived by sutherland s method 1970

colored solutions of the yang baxter equation from representations of uqgl 2 we study the hopf algebra structure and the highest weight representation of a multiparameter version of uqgl 2 the hopf algebra maps of this algebra are explicitly given we show that the multiparameter universal r matrix can be constructed directly as a quantum double intertwiner without using reshetikhin s twisting transformation we find there are two types highest weight representations for this algebra type a corresponds to the qeneric q and type b corresponds to the case that q is a root of unity when applying the representation theory to the multi parameter universal r matrix both standard and nonstandard colored solutions of the yang baxter equation are obtained

multiparametric quantum gl 2 lie bialgebras quantum r matrices and non relativistic limits multiparametric quantum deformations of gl 2 are studied through a complete classification of gl 2 lie bialgebra structures from these the non relativistic limit leading to harmonic oscillator lie bialgebras is implemented by means of a contraction procedure new quantum deformations of gl 2 together with their associated quantum r matrices are obtained and other known quantizations are recovered and classified several connections with integrable models are outlined

solving the two dimensional constant quantum yang baxter equation a detailed analysis of the constant quantum yang baxter equation rk1k2j1j2 rl1k3k1j3rl2l3k2k3 rk2k3j2j3 rk1l3j1k3rl1l2k1k2 in two dimensions is presented leading to an exhaustive list of its solutions the set of 64 equations for 16 unknowns was first reduced by hand to several subcases which were then solved by computer using the grobner basis methods each solution was then transformed into a canonical form based on the various trace matrices of r for final elimination of duplicates and subcases if we use homogeneous parametrization the solutions can be combined into 23 distinct cases modulo the well known c p and t reflections and rotations and scalings r q q r q q 1

variable elimination in chemical reaction networks with mass action kinetics we consider chemical reaction networks taken with mass action kinetics the steady states of such a system are solutions to a system of polynomial equations even for small systems the task of finding the solutions is daunting we develop an algebraic framework and procedure for linear elimination of variables the procedure reduces the variables in the system to a set of core variables by eliminating variables corresponding to a set of noninteracting species the steady states are parameterized algebraically by the core variables and a graphical condition is given that ensures that a steady state with positive core variables necessarily takes positive values for all variables further we characterize graphically the sets of eliminated variables that are constrained by a conservation law and show that this conservation law takes a specific form

solutions of yang baxter equations with colours standard and nonstandard colour extended solutions of ybe associated with g bn cn and dn are derived and the coloured birman wenzl algebra cb wa is established the authors point out that the cb wa still satisfies the redundance conditions of murakami 1989 for nonstandard solution they take the nontrivial colour solution of d2 as an example they find that the colour constraints induce a new solution with q4 1 the implication of this is not clear

a geometric proof of total positivity for spline interpolation abstract the total positivity of the spline collocation matrix is the basis of several important results in univariate spline theory this makes it desirable to provide as simple as possible a proof of this total positivity the proofs available in the literature don t qualify since these all rely on certain determinant identities which are not exactly intuitive the authors give a proof that uses nothing more than cramer s rule hard to avoid since total positivity is a statement about determinants and the geometrically obvious fact that a b spline can always be written as a positive combination of b splines on a finer knot sequence the geometric intuition appealed to here stems from the area of computer aided design in which a spline is constructed and manipulated through its b polygon a broken line whose vertices correspond to the b spline coefficients if a knot is added to provide greater potential flexibility the new b polygon is obtained by interpolation to the old this had led lane and riesenfeld to a proof of the variation diminishing property of the spline collocation matrix and is shown here to provide a proof of the total positivity as well

type i quantum superalgebras q supertrace and two variable link polynomials a new general eigenvalue formula for the eigenvalues of casimir invariants for the type i quantum superalgebras is applied to the construction of link polynomials associated with any finite dimensional unitary irrep for these algebras this affords a systematic construction of new two variable link polynomials associated with any finite dimensional irrep with a real highest weight for the type i quantum superalgebras in particular infinite families of nonequivalent two variable link polynomials are determined in fully explicit form

the universal r matrix and the yang baxter equation with parameters the authors formulate and demonstrate with some examples a method for obtaining solutions of the yang baxter equation with parameters

exotic quantum double its universal r matrix and their representations the exotic quantum double and its universal r matrix for the quantum yang baxter equation are constructed in terms of drinfeld s quantum double theory as a new quasitriangular hopf algebra it is different from those standard quantum doubles that are the q deformations for lie algebras or lie superalgebras by studying its representation theory many parameter representations of the exotic quantum double are obtained with an explicit example associated with lie algebra a2 the multiparameter r matrices for the quantum yang baxter equation can result from the universal r matrix of this exotic quantum double and these representations

on the new algebra related to the non standard r matrix the authors demonstrate that the new algebra associated to the non standard r matrix investigated previously by fei and yue 1993 is related to the su 2 q algebra by a simple transformation criteria which identify equivalent quantum algebra are given

coloured frt algebra and its yang baxterization leading to integrable models with non additive r matrices a colour representation of faddeev reshetikhin takhtajan frt algebra which in contrast to the standard case is related to the coloured braid group representation with generic values of q is presented explicit realizations of l or matrices occurring in this coloured variant of frt algebra are also obtained for the uq gl 2 quantized algebra though these realizations are found to depend manifestly on the colour parameters the underlying quantum group structure and associated co product are interestingly free from such dependence this allows us to perform the yang baxterization of the coloured frt algebra successfully which leads to the construction of an ancestor law operator associated with a new non additive type quantum r matrix through different realizations of this lax operator a new class of quantum integrable models representing colour generalizations of the well known models such as the lattice sine gordon model the ablowitz ladik model lattice and the derivative nonlinear schrodinger model etc is generated

new constant and trigonometric 4 4 solutions to the yang baxter equations a classification of triangular constant solutions of the yang baxter equations is performed the formulae for the baxterization of braid group representation are used for finding trigonometric solutions of the yang baxter equations from the constant ones some of the obtained solutions correspond to known solutions but several new ones are obtained as well the calculations confirm that the baxterization formulae for more than two eigenvalues of the r matrix are not universal

on the solutions of the yang baxter equations with general inhomogeneous eight vertex r matrix relations with zamolodchikov s tetrahedral algebra we present most general one parametric solutions of the yang baxter equations ybe for one spectral parameter dependent r ij u matrices of the six and eight vertex models where the only constraint is the particle number conservation by mod 2 a complete classification of the solutions is performed we have obtained also two spectral parameter dependent particular solutions r ij u v of ybe the application of the non homogeneous solutions to construction of zamolodchikov s tetrahedral algebra is discussed

positive solutions of positive linear systems easily verifiable sufficient conditions are obtained for the existence of a positive solution componentwise of a linear nonhomogeneous system of equations with positive coefficients

universal spectral parameter dependent lax operators for the drinfeld double of the dihedral group d3 two universal spectral parameter dependent lax operators are presented in terms of the elements of the drinfeld double d d3 of the dihedral group d3 applying representations of d d3 to these yields matrix solutions of the yang baxter equation with a spectral parameter

conditioning and accurate computations with pascal matrices a result on the ill conditioning of pascal matrices is proved however it is shown that bidiagonal factorizations of pascal matrices can be applied to perform computations with high relative accuracy

qr decomposition of almost strictly sign regular matrices in this paper l d u factorization of nonsingular sign regular and almost strictly sign regular matrices is analyzed besides nonsingular almost strictly sign regular matrices are characterized through the q r factorization illustrative numerical examples are included

trigonometric yang baxterization of coloured r matrix for a given coloured solution r lambda mu of the quantum yang baxter equation in appropriate form the authors present an explicit prescription to generate trigonometric solutions r lambda mu x of the yang baxter equation with spectral parameters x when the given r lambda mu admits the birman wenzl algebraic structure with colour they find that two types of the r lambda mu x are generated by such r lambda mu new explicit examples associated with the fundamental representations of an bn cn and dn are given in terms of this prescription

extended birman wenzl algebra and yang baxterization a new algebra a is presented by directly extending the birman wenzl algebra if a braid group representation with four distinct eigenvalues satisfies a then it can be yang baxterized to derive the solution of the yang baxter equation in terms of a standard scheme

the upper triangular solutions to the three state constant quantum yang baxter equation in this article we present all nonsingular upper triangular solutions to the constant quantum yang baxter equation rj1j2k1k2 rk1j3l1k3 rk2k3l2l3 rj2j3k2k3 rj1k3k1l3 rk1k2l1l2 in the three state case the upper triangular ansatz implies 729 equations for 45 variables fortunately many of the equations turned out to be simple allowing us to start breaking the problem into smaller ones in the end we had a total of 552 solutions but many of them were either inherited from two state solutions or subcases of others the final list contains 35 nontrivial solutions most of them new

more about the nonstandard r matrix associated with suq 2 the markov trace is constructed for the general r matrices associated with suq 2 at q a root of unity the relationship between the r matrices derived based on quantum algebra and those obtained by akutsu et al 1991 is clarified

almost strictly totally negative matrices a real matrix a a i j 1 i j n is said to be almost strictly totally negative if it is almost strictly sign regular with signature e 1 1 1 which is equivalent to the property that all its nontrivial minors are negative in this paper an algorithmic characterization of nonsingular almost strictly totally negative matrices is presented

the failure distribution in percolation models of breakdown the probability of finding a largest defect cluster of size n in a percolation network is calculated analytically using a new distribution function scaling equation from this result and the stress voltage enhancement at the tip of the most critical defect in the network the probability of failure in percolation models of breakdown is calculated for defect fractions less than the percolation point this distribution is found to be of the form exponential of an exponential numerical simulations on the two dimensional random fuse network confirm the new distribution function and convincingly distinguish between it and the weibull 1951 form most often used in the fitting of breakdown data

a note on graded yang baxter solutions as braid monoid invariants we construct two osp n mod 2m solutions of the graded yang baxter equation by using the algebraic braid monoid approach the factorizable s matrix interpretation of these solutions is also discussed

colored quantum universal enveloping algebras we define some new algebraic structures termed colored hopf algebras by combining the coalgebra structures and antipodes of a standard hopf algebra set h corresponding to some parameter set q with the transformations of an algebra isomorphism group g herein called color group such transformations are labeled by some color parameters taking values in a color set c we show that various classes of hopf algebras such as almost cocommutative coboundary quasitriangular and triangular ones can be extended into corresponding colored algebraic structures and that colored quasitriangular hopf algebras in particular are characterized by the existence of a colored universal r matrix satisfying the colored yang baxter equation the present definitions extend those previously introduced by ohtsuki which correspond to some substructures in those cases where the color group is abelian we apply the new concepts to construct colored quantum universal enveloping algebras of both semisimple and nonsemisimple lie algebras considering several examples with fixed or varying parameters as a by product some of the matrix representations of colored universal r matrices derived in the present paper provide new solutions of the colored yang baxter equation which might be of interest in the context of integrable models

total positivity and neville elimination abstract neville elimination is described in terms of schur complements of matrices and used to improve some well known characterizations of totally positive and strictly totally positive matrices

yang baxterization of the eight vertex model the braid group approach the braid group representation bgr for the eight vertex model is solved for the case in which the total spins are not conserved a yang baxterization scheme is applied to obtain from these bgr the spectral dependent solution they are found to correspond to the free fermion and the disorder point solutions

exactly solvable quantum spin ladders associated with the orthogonal and symplectic lie algebras we extend the results of spin ladder models associated with the lie algebras su 2 n to the case of the orthogonal and symplectic algebras o 2 n sp 2 n where n is the number of legs for the system two classes of models are found whose symmetry either orthogonal or symplectic has an explicit n dependence integrability of these models is shown for an arbitrary coupling of xx type rung interactions and applied magnetic field term

new solutions of yang baxter equations birman wenzl algebra and quantum group structures new braid group representations associated with the fundamental representations of bn cn and dn are derived they are shown to satisfy birman wenzl algebra by yang baxterization the authors obtain new solutions of yang baxter equations including the twisted extensions quantum group structures related to these new solutions are explicitly given

on nonsingular sign regular matrices abstract an m n matrix a is sign regular if for each k 1 k min m n all k k submatrices of a have determinant with the same nonstrict sign the zero pattern of nonsingular sign regular matrices is analyzed it is proved that the number of zero entries which can appear in a nonsingular sign regular matrix depends on its signature a matrix is totally nonpositive if all its minors are nonpositive a test for recognizing nonsingular totally nonpositive matrices is also provided

a non standard quantum double as the l state boson algebra and its r matrices for the quantum yang baxter equation in this paper we construct a new quantum double by endowing the l state boson algebra with a non trivial hopf algebra structure which is not a q deformation of the lie algebra or superalgebra the universal r matrix for the yang baxter equation associated with this new quantum group structure is obtained explicitly by building the representations of this quantum double we obtain some r matrices which can result in new representations of the braid group

new hierarchy of colored braid group representations novel solutions of the yang baxter relation for a series of multistate vertex models are presented in the braid group limit the obtained family of solutions gives a sequence of colored braid group representations possible generalizations of the multivariable alexander polynomial are discussed

graded solutions of the yang baxter relation and link polynomials from a family of graded solvable models the authors derive representations of the braid group associated with the lie superalgebra gl m mod n and give explicitly a general form of the markov traces on the representations the braid operators thus obtained satisfy the hecke algebra the authors construct composite solvable models and obtain link polynomials from the braid operators for the composite models

full rank factorization in quasi ldu form of totally nonpositive rectangular matrices abstract let a a i j r n m be a totally nonpositive matrix with rank a r min n m and a 11 0 in this paper we obtain a characterization in terms of the full rank factorization in quasi ldu form that is a l d u where l r n r is a block lower echelon matrix u r r m is a unit upper echelon totally positive matrix and d r r r is a diagonal matrix with rank l rank u rank d r we use this quasi ldu decomposition to construct the quasi bidiagonal factorization of a moreover some properties about these matrices are studied

non birman wenzl algebraic properties and redundancy of exotic enhanced yang baxter operator for spin model in this paper we explicitly construct the markov trace for the general coloured exotic braid group representations bgr with spin j it is verified that the bgr for j 1 is redundant in the sense of murakami 1990 but no birman wenzl algebra

the approximation of a totally positive band matrix by a strictly banded totally positive one every nonsingular totally positive m banded matrix is shown to be the product of m totally positive one banded matrices and therefore the limit of strictly m banded totally positive matrices this result is then extended to bi infinite m banded totally positive matrices with linearly independent rows and columns in the process such matrices are shown to possess at least one diagonal whose principal sections are all nonzero as a consequence such matrices are seen to be approximable by strictly m banded totally positive ones

random walks on braid groups brownian bridges complexity and statistics we investigate the limit behaviour of random walks on some non commutative discrete groups related to knot theory namely we study the connection between the limit behaviour of the lyapunov exponent of products of non commutative random matrices generators of the braid group and the asymptotics of powers of the algebraic invariants of randomly generated knots we turn the simplest problems of knot statistics into the context of random walks on hyperbolic groups we also consider the limit distribution of brownian bridges on so called locally non commutative groups

integrable spin chains associated with slq n and slp q n the hopf structure of the central extension of the uq sl n algebra is considered the intertwine matrix induces new integrable chain models we show the relation of these models and the biparametric spin chain slp q n models the cases n 2 are n 3 are discussed and for n 2 we obtain the model of dasgupta and chowdhury 1993 the case n 3 is solved by the nested bethe ansatz method and the dependence of the bethe equations on the second parameter introduced is demonstrated

truncated global transfer matrix trigonometric goryachev chaplygin gyrostat the rtt relation with truncation is solved for the r matrix associated with the six vertex model it turns out that the finite expansion of the global solution of the transfer matrix t u in terms of the spectral parameter u can be realized by the defined algebra formed by and the non commutative coordinates the hamiltonian of the system has been found which is the trigonometric deformation of the goryachev chaplygin gyrostat

a test for strict sign regularity a characterization of strict sign regular matrices is obtained it is given in an algorithmic form which allows the easy construction of a test to check if a matrix is strictly sign regular the test is based on the neville elimination of several submatrices of a and requires less computational work than those which can be derived from other previously known characterizations of these matrices

r matrices of three state hamiltonians solvable by coordinate bethe ansatz we review some of the strategies that can be implemented to infer an r matrix from the knowledge of its hamiltonian we apply them to the classification achieved in crampe frappat and ragoucy j phys a 46 405001 2013 on three state u 1 invariant hamiltonians solvable by coordinate bethe ansatz focusing on models for which the s matrix is not trivial for the 19 vertex solutions we recover the r matrices of the well known zamolodchikov fateev and izergin korepin models we point out that the generalized bariev hamiltonian is related to both main and special branches studied by martins in nucl phys b 874 243 2013 that we prove to generate the same hamiltonian the 19 vertex spr model still resists to the analysis although we are able to state some no go theorems on its r matrix for 17 vertex hamiltonians we produce a new r matrix

yang baxterization of braid group representations for a given braid group representation bgr a process of the yang baxterization is formulated to generate solutions of the yang baxter equation ybe when a bgr admits the birman wenzl bw algebraic structure this process can be explicitly passed through and two types of trigonometric solutions of ybe are generated from such a bgr these two solutions have the essential difference to each other and both of them preserve the crossing symmetry property if the given bgr has by taking certain reduction on the bw algebra the rational solution is also generated a practical condition to judge whether a bgr satisfies the bw algebra is given from which one finds that not only the familiar bgrs of 5 7 9 but also some new ones obtained recently in 12 have the bw structure thus they can be explicitly yang baxterized to solutions of the ybe

integrable boundary conditions for multi species asep the first result of the present paper is to provide classes of explicitsolutions for integrable boundary matrices for the multi species asep with anarbitrary number of species all the solutions we have obtained can be seen as representations of a newalgebra that contains the boundary hecke algebra the boundary hecke algebra isnot sufficient to build these solutions this is the second result of ourpaper

exactly soluble isotropic spin ladder models the undeformed limit of the dilute two colour braid monoid algebra gives a natural basis for the description of spin ladder models and allows different baxterization ansatze based on this observation we find the complete classification of exactly soluble generalized isotropic spin ladder models

representations of the quantum doubles of finite group algebras and spectral parameter dependent solutions of the yang baxter equation quantum doubles of finite group algebras form a class of quasitriangular hopf algebras that algebraically solve the yang baxter equation each representation of the quantum double then gives a matrix solution of the yang baxter equation such solutions do not depend on a spectral parameter and to date there has been little investigation into extending these solutions such that they do depend on a spectral parameter here we first explicitly construct the matrix elements of the generators for all irreducible representations of quantum doubles of the dihedral groups dn these results may be used to determine constant solutions of the yang baxter equation we then discuss baxterization ansatze to obtain solutions of the yang baxter equation with a spectral parameter and give several examples including a new 21 vertex model we also describe this approach in terms of minimal dimensional representations of the quantum doubles of the alternating group a4 and the symmetric group s4

almost strictly sign regular matrices and neville elimination with two determinant pivoting in 2007 cortes and pena introduced a pivoting strategy for the neville elimination of nonsingular sign regular matrices and called it two determinant pivoting neville elimination has been very useful for obtaining theoretical and practical properties for totally positive negative matrices and other related types of matrices a real matrix is said to be almost strictly sign regular if all its nontrivial minors of the same order have the same strict sign in this paper some nice properties related with the application of neville elimination with two determinant pivoting strategy to almost strictly sign regular matrices are presented

quantum harmonic oscillator algebra and link invariants associated with the q deformation of the harmonic oscillator algebra we define an infinite dimensional braid group representation on the hilbert space of the harmonic oscillator and an extended yang baxter system in the sense of turaev the corresponding link invariant is computed in some particular cases and coincides with the inverse of the alexander conway polynomial the r matrix of uq h4 can be interpreted as defining a baxterization of the intertwiners for semicyclic representations of su 2 q at q e2 i n in the n limit finally we define new multicolored braid group representations and study their relation to the multivariable alexander conway polynomial

a factorization theorem for banded matrices in this paper we prove a factorization theorem for strictly m banded totally positive matrices we show that such a matrix is a product of m one banded matrices with positive entries a bi infinite matrix a ai i ca i and ai i n ai i o these matrices arise quite freqiently in applications and recently the have been the subject of several independent investigations 2 3 in this paper we prove a factorization theorem for strictly m handed totally positive matrices we show that such a matrix is a product of m one banded matrices with positive entries let us begin by recalling that a matrix a is totally positive if and only if ull its minors are nonnegative

quantized braided groups algebras that represent a generalization of both quantum groups quantum supergroups and braided groups are defined they are given by a pair of solutions of the yang baxter equation that satisfy some additional conditions several examples are presented

graphical criteria for positive solutions to linear systems abstract we study linear systems of equations with coefficients in a generic partially ordered ring r and a unique solution and seek conditions for the solution to be nonnegative that is every component of the solution is a quotient of two nonnegative elements in r the requirement of a nonnegative solution arises typically in applications for example in biology and ecology where quantities of interest are concentrations and abundances we provide novel conditions on a labeled multidigraph associated with the linear system that guarantee the solution to be nonnegative furthermore we study a generalization of the first class of linear systems where the coefficient matrix has a specific block form and provide analogous conditions for nonnegativity of the solution similarly based on a labeled multidigraph the latter scenario arises naturally in chemical reaction network theory when studying full or partial parameterizations of the positive part of the steady state variety of a polynomial dynamical system in the concentrations of the molecular species

bethe subalgebras in affine birman murakami wenzl algebras and flat connections for q kz equations commutative sets of jucys murphy elements for affine braid groups of types were defined construction of r matrix representations of the affine braid group of type and its distinguished commutative subgroup generated by the type jucys murphy elements are given we describe a general method to produce flat connections for the two boundary quantum knizhnik zamolodchikov equations as necessary conditions for sklyanin s type transfer matrix associated with the two boundary multicomponent zamolodchikov algebra to be invariant under the action of the type jucys murphy elements we specify our general construction to the case of the birman murakami wenzl algebras bmw algebras for short as an application we suggest a baxterization of the dunkl cherednik elements in the double affine hecke algebra of type a

invariant tangles of coloured non standard solutions of braid relations the invariant tangles for murakami s coloured solution 1990 of braid relations are explicitly calculated in terms of the kauffman saleur fermionic integral 1991 a more general coloured solution r c1 c2 of braid group representation is obtained the authors verify that such r c1 c2 satisfies all the redundant conditions presented by murakami they thus derive invariant alexander link polynomials for the new coloured solution

the yang baxter equation and invariants of links on considere le fait que l on peut construire des invariants d isotopie p et f pour des liens en utilisant certaines solutions des equations de yang baxter

universal baxterization for z graded hopf algebras we present a method for baxterizing solutions of the constant yang baxter equation associated with z graded hopf algebras to demonstrate the approach we provide examples for the taft algebras and the quantum group u q sl 2

a nonlinear deformed su 2 algebra with a two color quasitriangular hopf structure nonlinear deformations of the enveloping algebra of su 2 involving two arbitrary functions of j0 and generalizing the witten algebra were introduced some time ago by delbecq and quesne in the present paper the problem of endowing some of them with a hopf algebraic structure is addressed by studying in detail a specific example referred to as aq 1 this algebra is shown to possess two series of n 1 dimensional unitary irreducible representations where n 0 1 2 to allow the coupling of any two such representations a generalization of the standard hopf axioms is proposed by proceeding in two steps in the first one a variant and extension of the deforming functional technique is introduced variant because a map between two deformed algebras suq 2 and aq 1 is considered instead of a map between a lie algebra and a deformed one and extension because use is made of a two valued functional whose inverse is singular as a result the hopf structure of suq 2 is carried over to aq 1 ther

nonsingular almost strictly sign regular matrices abstract the class of nonsingular almost strictly totally positive matrices has been characterized m gasca j m pena characterizations and decompositions of almost strictly positive matrices siam j matrix anal appl 28 2006 1 8 in this paper we discuss the class of almost strictly sign regular matrices that includes almost strictly totally positive matrices a characterization is provided for these matrices in terms of their nontrivial minors using consecutive rows and consecutive columns in particular we present a characterization of certain almost strictly sign regular matrices in terms of a very reduced number of boundary almost trivial minors

a new braid like algebra for baxterisation we introduce a new baxterisation for r matrices that depend separately on two spectral parameters the baxterisation is based on a new algebra close to but different from the braid group we study representations of this new algebra on the vector space mathbb c m otimes n when the generators act locally the ones for m 2 are completely classified we also introduce some representations for generic m they allow us to recover the r matrix of the multi species generalization of the totally asymmetric simple exclusion process with different hopping rates

multi colour braid monoid algebras we define multi colour generalizations of braid monoid algebras and present explicit matrix representations which are related to two dimensional exactly solvable lattice models of statistical mechanics in particular we show that the two colour braid monoid algebra describes the yang baxter algebra of the critical dilute a d e models which were recently introduced by warnaar nienhuis and seaton 1992 as well as by roche 1992 these and other solvable models related to dense and dilute loop models are discussed in detail and it is shown that the solvability is a direct consequence of the algebraic structure it is conjectured that the baxterization of general multi colour braid monoid algebras will lead to the construction of further solvable lattice models

equivalent isotropic osp 2 2 spin chains and its bethe ansatz analysis in this paper we discuss the equivalence between two integrable and isotropic osp 2 2 chains via the braid monoid approach we use the analytical bethe ansatz approach in order to solve the spectrum of these systems the ground state is parametrized by a special structure of the bethe ansatz roots their interpretation in terms of correlated fermionic models is briefly discussed