We present the matrix U. The 9 × 9 U matrix is a representation of specialized Temperley-Lieb algebra. Based on which, a unitary R matrix is generated via the Yang-Baxterization approach. The 9 × 9 R matr...We present the matrix U. The 9 × 9 U matrix is a representation of specialized Temperley-Lieb algebra. Based on which, a unitary R matrix is generated via the Yang-Baxterization approach. The 9 × 9 R matrix, a solution of the Yang-Baxter equation, is universal for quantum entanglement.展开更多
The authors first construct an explicit minimal projective bimodule resolution(P, δ) of the Temperley-Lieb algebra A, and then apply it to calculate the Hochschild cohomology groups and the cup product of the Hochsch...The authors first construct an explicit minimal projective bimodule resolution(P, δ) of the Temperley-Lieb algebra A, and then apply it to calculate the Hochschild cohomology groups and the cup product of the Hochschild cohomology ring of A based on a comultiplicative map Δ:P → PAP. As a consequence, the authors determine the multiplicative structure of Hochschild cohomology rings of both Temperley-Lieb algebras and representation-finite q-Schur algebras under the cup product by giving an explicit presentation by generators and relations.展开更多
The authors study the properties of virtual Temperley-Lieb algebra and show how the f-polynomial of virtual knot can be derived from a representation of the virtual braid group into the virtual Temperley-Lieb algebra,...The authors study the properties of virtual Temperley-Lieb algebra and show how the f-polynomial of virtual knot can be derived from a representation of the virtual braid group into the virtual Temperley-Lieb algebra, which is an approach similar to Jones' s original construction.展开更多
基金supported by the Science Foundation of the Education Department of Jilin Province,China (Grant No.2011JTY11)
文摘We present the matrix U. The 9 × 9 U matrix is a representation of specialized Temperley-Lieb algebra. Based on which, a unitary R matrix is generated via the Yang-Baxterization approach. The 9 × 9 R matrix, a solution of the Yang-Baxter equation, is universal for quantum entanglement.
基金supported by the National Natural Science Foundation of China(Nos.11171325,11371186,11301161)the Research Foundation of Education Bureau of Hubei Province of China(No.Q20131009)
文摘The authors first construct an explicit minimal projective bimodule resolution(P, δ) of the Temperley-Lieb algebra A, and then apply it to calculate the Hochschild cohomology groups and the cup product of the Hochschild cohomology ring of A based on a comultiplicative map Δ:P → PAP. As a consequence, the authors determine the multiplicative structure of Hochschild cohomology rings of both Temperley-Lieb algebras and representation-finite q-Schur algebras under the cup product by giving an explicit presentation by generators and relations.
基金supported by the National Natural Sciences Foundation of China(Nos.11329101,11431009,11301135,11201314,11302136,A2014210062)the Excellent Young Scientist Fund of Shijiazhuang Tiedao University
文摘The authors study the properties of virtual Temperley-Lieb algebra and show how the f-polynomial of virtual knot can be derived from a representation of the virtual braid group into the virtual Temperley-Lieb algebra, which is an approach similar to Jones' s original construction.
基金During the preparation of this paper,the authors were supported by NSFC(No.11671139),STCSM(No.13dz2260400)the Fundamental Research Funds for the Central Universities.The authors thanks their supervisor Prof.Guodong Zhou for his valuable suggestions and a lot of help.
文摘We determine the Gerstenhaber algebra structure on the Hochschild cohomology ring of Temperley–Lieb algebras in this paper.
