Steenrod operations are cohomology operations that are themselves natural transformations between cohomology functors. There are two distinct types of steenrod operations initially constructed by Norman Steenrod and called Steenrod squares and reduced p-th power operations usually denoted Sq and p^{i} respectively. Since their creation, it has been proved that these operations can be constructed in the cohomology of many algebraic structures, for instance in the cohomology of simplicial restricted Lie algebras, the cohomology of cocommutative Hopf algebras and the homology of infinite loop space. Later on J. P. May developped a general algebraic setting in which all the above cases can be studied. In this work we consider a cyclic group π of oder a fixed prime p and combine theπ-strongly homotopy commutative Hopf algebra structure to the May’s approach with the aim to build these natural transformations on the Hochschild cohomology groups. Moreover we give under some conditions a link of these natural transformations with the Gerstenhaber algebra structure.
Published in | Pure and Applied Mathematics Journal (Volume 9, Issue 2) |
DOI | 10.11648/j.pamj.20200902.12 |
Page(s) | 37-45 |
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π-Strongly Homotopy Commutative Hopf Algebra, Cohomology Operations, Gerstenhaber Algebra
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APA Style
Calvin Tcheka. (2020). Cohomology Operations andπ-Strongly Homotopy Commutative Hopf Algebra. Pure and Applied Mathematics Journal, 9(2), 37-45. https://doi.org/10.11648/j.pamj.20200902.12
ACS Style
Calvin Tcheka. Cohomology Operations andπ-Strongly Homotopy Commutative Hopf Algebra. Pure Appl. Math. J. 2020, 9(2), 37-45. doi: 10.11648/j.pamj.20200902.12
AMA Style
Calvin Tcheka. Cohomology Operations andπ-Strongly Homotopy Commutative Hopf Algebra. Pure Appl Math J. 2020;9(2):37-45. doi: 10.11648/j.pamj.20200902.12
@article{10.11648/j.pamj.20200902.12, author = {Calvin Tcheka}, title = {Cohomology Operations andπ-Strongly Homotopy Commutative Hopf Algebra}, journal = {Pure and Applied Mathematics Journal}, volume = {9}, number = {2}, pages = {37-45}, doi = {10.11648/j.pamj.20200902.12}, url = {https://doi.org/10.11648/j.pamj.20200902.12}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20200902.12}, abstract = {Steenrod operations are cohomology operations that are themselves natural transformations between cohomology functors. There are two distinct types of steenrod operations initially constructed by Norman Steenrod and called Steenrod squares and reduced p-th power operations usually denoted Sq and pi respectively. Since their creation, it has been proved that these operations can be constructed in the cohomology of many algebraic structures, for instance in the cohomology of simplicial restricted Lie algebras, the cohomology of cocommutative Hopf algebras and the homology of infinite loop space. Later on J. P. May developped a general algebraic setting in which all the above cases can be studied. In this work we consider a cyclic group π of oder a fixed prime p and combine theπ-strongly homotopy commutative Hopf algebra structure to the May’s approach with the aim to build these natural transformations on the Hochschild cohomology groups. Moreover we give under some conditions a link of these natural transformations with the Gerstenhaber algebra structure.}, year = {2020} }
TY - JOUR T1 - Cohomology Operations andπ-Strongly Homotopy Commutative Hopf Algebra AU - Calvin Tcheka Y1 - 2020/04/23 PY - 2020 N1 - https://doi.org/10.11648/j.pamj.20200902.12 DO - 10.11648/j.pamj.20200902.12 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 37 EP - 45 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.20200902.12 AB - Steenrod operations are cohomology operations that are themselves natural transformations between cohomology functors. There are two distinct types of steenrod operations initially constructed by Norman Steenrod and called Steenrod squares and reduced p-th power operations usually denoted Sq and pi respectively. Since their creation, it has been proved that these operations can be constructed in the cohomology of many algebraic structures, for instance in the cohomology of simplicial restricted Lie algebras, the cohomology of cocommutative Hopf algebras and the homology of infinite loop space. Later on J. P. May developped a general algebraic setting in which all the above cases can be studied. In this work we consider a cyclic group π of oder a fixed prime p and combine theπ-strongly homotopy commutative Hopf algebra structure to the May’s approach with the aim to build these natural transformations on the Hochschild cohomology groups. Moreover we give under some conditions a link of these natural transformations with the Gerstenhaber algebra structure. VL - 9 IS - 2 ER -