Displaying similar documents to “New categorifications of the chromatic and dichromatic polynomials for graphs”

A colored Khovanov bicomplex

Noboru Ito (2014)

Banach Center Publications

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In this note, we prove the existence of a tri-graded Khovanov-type bicomplex (Theorem 1.2). The graded Euler characteristic of the total complex associated with this bicomplex is the colored Jones polynomial of a link. The first grading of the bicomplex is a homological one derived from cabling of the link (i.e., replacing a strand of the link by several parallel strands); the second grading is related to the homological grading of ordinary Khovanov homology; finally, the third grading...

On Ordinary and Z2-graded Polynomial Identities of the Grassmann Algebra

Ribeiro Tomaz da Silva, Viviane (2012)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: Primary: 16R10, Secondary: 16W55. The main purpose of this paper is to provide a survey of results concerning the ordinary and Z2-graded polynomial identities of the infinite dimensional Grassmann algebra over a field of characteristic zero, as well as of its sequences of ordinary and Z2-graded codimensions and cocharacters. We also intend to describe briefly the techniques used by the authors in order to illustrate some important...

On graded P-compactly packed modules

Khaldoun Al-Zoubi, Imad Jaradat, Mohammed Al-Dolat (2015)

Open Mathematics

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Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper, we introduce the concept of graded P-compactly packed modules and we give a number of results concerning such graded modules. In fact, our objective is to investigate graded P-compactly packed modules and examine in particular when graded R-modules are P-compactly packed. Finally, we introduce the concept of graded finitely P-compactly packed modules and give a number of its...

Z2-Graded Polynomial Identities for Superalgebras of Block-Triangular Matrices

Di Vincenzo, Onofrio (2004)

Serdica Mathematical Journal

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000 Mathematics Subject Classification: Primary 16R50, Secondary 16W55. We present some results about the Z2-graded polynomial identities of block-triangular matrix superalgebras R[[A M],[0 B]]. In particular, we describe conditions for the T2-ideal of a such superalgebra to be factorable as the product T2(A)T2(B). Moreover, we give formulas for computing the sequence of the graded cocharacters of R in some interesting case. Partially supported by MURST COFIN...

Gradings and Graded Identities for the Matrix Algebra of Order Two in Characteristic 2

Koshlukov, Plamen, César dos Reis, Júlio (2012)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: 16R10, 16R99, 16W50. Let K be an infinite field and let M2(K) be the matrix algebra of order two over K. The polynomial identities of M2(K) are known whenever the characteristic of K is different from 2. The algebra M2(K) admits a natural grading by the cyclic group of order 2; the graded identities for this grading are known as well. But M2(K) admits other gradings that depend on the field and on its characteristic. Here we describe...

Some properties of graded comultiplication modules

Khaldoun Al-Zoubi, Amani Al-Qderat (2017)

Open Mathematics

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Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper we will obtain some results concerning the graded comultiplication modules over a commutative graded ring.

A Basis for Z-Graded Identities of Matrices over Infinite Fields

Azevedo, Sergio (2003)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 16R10, 16R20, 16R50 The algebra Mn(K) of the matrices n × n over a field K can be regarded as a Z-graded algebra. In this paper, it is proved that if K is an infinite field, all the Z-graded polynomial identities of Mn(K) follow from the identities: x = 0, |α(x)| ≥ n, xy = yx, α(x) = α(y) = 0, xyz = zyx, α(x) = −α(y) = α(z ), where α is the degree of the corresponding variable. This is a generalization of a result of Vasilovsky about...