We present a general construction producing a unitary corepresentation of a multiplier Hopf algebra in itself and study RR-corepresentations of twisted tensor coproduct multiplier Hopf algebra. Then we investigate som...We present a general construction producing a unitary corepresentation of a multiplier Hopf algebra in itself and study RR-corepresentations of twisted tensor coproduct multiplier Hopf algebra. Then we investigate some properties of functors, integrals and morphisms related to the categories of the crossed modules and covariant modules over multiplier Hopf algebras. By doing so, we can apply our theory to the case of group-cograded multiplier Hopf algebras, in particular, the case of Hopf group-coalgebras.展开更多
Let H and its dual H* be finite dimensional semisimple Hopf algebras. In this paper, we firstly prove that the derived representation types of an algebra A and the crossed product algebra A#σH are coincident. This is...Let H and its dual H* be finite dimensional semisimple Hopf algebras. In this paper, we firstly prove that the derived representation types of an algebra A and the crossed product algebra A#σH are coincident. This is an improvement of the conclusion about representation type of an algebra in Li and Zhang [Sci China Ser A, 2006, 50: 1-13]. Secondly, we give the relationship between Gorenstein projective modules over A and that over A#σH. Then, using this result, it is proven that A is a finite dimensional CM-finite Gorenstein algebra if and only if so is A#σH.展开更多
Y. Doi has investigated the H-comodule algebra since 1983. The structure theorem of cleft H-comodule algebra was given by Y. Doi and M. Takeuchi in 1986, i. e. if A is a cleft H-comodule algebra then A≌A<sub>0&...Y. Doi has investigated the H-comodule algebra since 1983. The structure theorem of cleft H-comodule algebra was given by Y. Doi and M. Takeuchi in 1986, i. e. if A is a cleft H-comodule algebra then A≌A<sub>0</sub>#<sub>σ</sub>H as algebra. The dual notion of H-comodule algebra is H-module coalgebra. Y. Doi also studied the H-module coalgebra. However, he did not obtain the structure theorem of cocleft H-module coalgebra. In this note we introduce crossed coproducts which are the dual notion展开更多
In this paper,we generalize the Takesaki-Takai duality theorem in Hilbert C~*-modules; that is to say,if (H,V,U) is a Kac-system,where H is a Hilbert space,V is a multiplicative unitary operator on H(?)H and U is a un...In this paper,we generalize the Takesaki-Takai duality theorem in Hilbert C~*-modules; that is to say,if (H,V,U) is a Kac-system,where H is a Hilbert space,V is a multiplicative unitary operator on H(?)H and U is a unitary operator on H,and if E is an (?)-compatible Hilbert (?)-module, then E×(?)×(?)K(H),where K(H) is the set of all compact operators on H,and (?) and (?) are Hopf C~*-algebras corresponding to the Kac-system (H,V,U).展开更多
In this article, we introduce the notions of restricted Lie 2-algebras and crossed modules of restricted Lie algebras, and give a series of examples of restricted Lie 2-algebras. We also construct restricted Lie 2-alg...In this article, we introduce the notions of restricted Lie 2-algebras and crossed modules of restricted Lie algebras, and give a series of examples of restricted Lie 2-algebras. We also construct restricted Lie 2-algebras from A(m)-algebras, restricted Leibniz algebras, restricted right-symmetric algebras. Finally, we prove that there is a one-to-one correspondence between strict restricted Lie 2-algebras and crossed modules of restricted Lie algebras.展开更多
In this note we first show that if H is a finite-dimensional Hopf algebra in a group Yetter-Drinfel'd category L^LyD(π) over a crossed Hopf group-coalgebra L, then its dual H^* is also a Hopf algebra in the categ...In this note we first show that if H is a finite-dimensional Hopf algebra in a group Yetter-Drinfel'd category L^LyD(π) over a crossed Hopf group-coalgebra L, then its dual H^* is also a Hopf algebra in the category L^LyD(π). Then we establish the fundamental theorem of Hopf modules for H in the category L^LyD(π).展开更多
Human posture estimation is a prominent research topic in the fields of human-com-puter interaction,motion recognition,and other intelligent applications.However,achieving highaccuracy in key point localization,which ...Human posture estimation is a prominent research topic in the fields of human-com-puter interaction,motion recognition,and other intelligent applications.However,achieving highaccuracy in key point localization,which is crucial for intelligent applications,contradicts the lowdetection accuracy of human posture detection models in practical scenarios.To address this issue,a human pose estimation network called AT-HRNet has been proposed,which combines convolu-tional self-attention and cross-dimensional feature transformation.AT-HRNet captures significantfeature information from various regions in an adaptive manner,aggregating them through convolu-tional operations within the local receptive domain.The residual structures TripNeck and Trip-Block of the high-resolution network are designed to further refine the key point locations,wherethe attention weight is adjusted by a cross-dimensional interaction to obtain more features.To vali-date the effectiveness of this network,AT-HRNet was evaluated using the COCO2017 dataset.Theresults show that AT-HRNet outperforms HRNet by improving 3.2%in mAP,4.0%in AP75,and3.9%in AP^(M).This suggests that AT-HRNet can offer more beneficial solutions for human posture estimation.展开更多
基金Supported by National Natural Science Foundation of China (Grant No. 10871042) the Research Fund for the Doctoral Program of Higher Education (Grant No. 20060286006)+1 种基金 Natural Science Foundation of Jiangsu Province (Grant No. BK2009258)the Key Project of Chinese Ministry of Education of China (Grant No.108154)
文摘We present a general construction producing a unitary corepresentation of a multiplier Hopf algebra in itself and study RR-corepresentations of twisted tensor coproduct multiplier Hopf algebra. Then we investigate some properties of functors, integrals and morphisms related to the categories of the crossed modules and covariant modules over multiplier Hopf algebras. By doing so, we can apply our theory to the case of group-cograded multiplier Hopf algebras, in particular, the case of Hopf group-coalgebras.
基金supported by National Natural Science Foundation of China (Grant No.11171296)the Zhejiang Provincial Natural Science Foundation of China (Grant No. D7080064)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110101110010)
文摘Let H and its dual H* be finite dimensional semisimple Hopf algebras. In this paper, we firstly prove that the derived representation types of an algebra A and the crossed product algebra A#σH are coincident. This is an improvement of the conclusion about representation type of an algebra in Li and Zhang [Sci China Ser A, 2006, 50: 1-13]. Secondly, we give the relationship between Gorenstein projective modules over A and that over A#σH. Then, using this result, it is proven that A is a finite dimensional CM-finite Gorenstein algebra if and only if so is A#σH.
文摘Y. Doi has investigated the H-comodule algebra since 1983. The structure theorem of cleft H-comodule algebra was given by Y. Doi and M. Takeuchi in 1986, i. e. if A is a cleft H-comodule algebra then A≌A<sub>0</sub>#<sub>σ</sub>H as algebra. The dual notion of H-comodule algebra is H-module coalgebra. Y. Doi also studied the H-module coalgebra. However, he did not obtain the structure theorem of cocleft H-module coalgebra. In this note we introduce crossed coproducts which are the dual notion
基金Supported by NSF 10301004,NSF 10171098Yantai University PHD Foundation SX03B14
文摘In this paper,we generalize the Takesaki-Takai duality theorem in Hilbert C~*-modules; that is to say,if (H,V,U) is a Kac-system,where H is a Hilbert space,V is a multiplicative unitary operator on H(?)H and U is a unitary operator on H,and if E is an (?)-compatible Hilbert (?)-module, then E×(?)×(?)K(H),where K(H) is the set of all compact operators on H,and (?) and (?) are Hopf C~*-algebras corresponding to the Kac-system (H,V,U).
基金Supported by ZJNSF(Grant Nos.LY17A010015 and LZ14A010001)NNSF(Grant No.11171296)
文摘In this article, we introduce the notions of restricted Lie 2-algebras and crossed modules of restricted Lie algebras, and give a series of examples of restricted Lie 2-algebras. We also construct restricted Lie 2-algebras from A(m)-algebras, restricted Leibniz algebras, restricted right-symmetric algebras. Finally, we prove that there is a one-to-one correspondence between strict restricted Lie 2-algebras and crossed modules of restricted Lie algebras.
基金the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20060286006) the National Natural Science Foundation of China (No. 10571026).
文摘In this note we first show that if H is a finite-dimensional Hopf algebra in a group Yetter-Drinfel'd category L^LyD(π) over a crossed Hopf group-coalgebra L, then its dual H^* is also a Hopf algebra in the category L^LyD(π). Then we establish the fundamental theorem of Hopf modules for H in the category L^LyD(π).
基金the National Natural Science Foundation of China(No.61975015)the Research and Innovation Project for Graduate Students at Zhongyuan University of Technology(No.YKY2024ZK14).
文摘Human posture estimation is a prominent research topic in the fields of human-com-puter interaction,motion recognition,and other intelligent applications.However,achieving highaccuracy in key point localization,which is crucial for intelligent applications,contradicts the lowdetection accuracy of human posture detection models in practical scenarios.To address this issue,a human pose estimation network called AT-HRNet has been proposed,which combines convolu-tional self-attention and cross-dimensional feature transformation.AT-HRNet captures significantfeature information from various regions in an adaptive manner,aggregating them through convolu-tional operations within the local receptive domain.The residual structures TripNeck and Trip-Block of the high-resolution network are designed to further refine the key point locations,wherethe attention weight is adjusted by a cross-dimensional interaction to obtain more features.To vali-date the effectiveness of this network,AT-HRNet was evaluated using the COCO2017 dataset.Theresults show that AT-HRNet outperforms HRNet by improving 3.2%in mAP,4.0%in AP75,and3.9%in AP^(M).This suggests that AT-HRNet can offer more beneficial solutions for human posture estimation.