Deformations of Quantum Symmetric Algebras Extended by Groups
MetadataShow full item record
The study of deformations of an algebra has been a topic of interest for quite some time, since it allows us to not only produce new algebras but also better understand the original algebra. Given an algebra, finding all its deformations is, if at all possible, quite a challenging problem. For this reason, several specializations of this question have been proposed. For instance, some authors concentrate their efforts in the study of deformations of an algebra arising from an action of a Hopf algebra. The purpose of this dissertation is to discuss a general construction of a deformation of a smash product algebra coming from an action of a particular Hopf algebra. This Hopf algebra is generated by skew-primitive and group-like elements, and depends on a complex parameter. The smash product algebra is defined on the quantum symmetric algebra of a nite-dimensional vector space and a group. In particular, an application of this result has enabled us to find a deformation of such a smash product algebra which is, to the best of our knowledge, the first known example of a deformation in which the new relations in the deformed algebra involve elements of the original vector space. Finally, using Hochschild cohomology, we show that these deformations are nontrivial.
Subjectalgebraic deformation theory
Hopf module algebras
quantum symmetric algebras
smash product algebras
Shakalli Tang, Jeanette (2012). Deformations of Quantum Symmetric Algebras Extended by Groups. Doctoral dissertation, Texas A&M University. Available electronically from
Showing items related by title, author, creator and subject.
Prediction of mathematics 102 grades from high school algebra grades and the cooperative elementary algebra test scores Oldham, Eldred Beamon (Texas A&M University, 1962)Not available
Mai, Stefan (2009-06-09)As miniaturization of computer components is approaching the limits of physics, researchers in computer architecture are looking for less conventional means to perpetuate Moore's law. Recent trends in hardware ve been ...
Anderson, Latoya (2013-12-09)This study examined validity and reliability of an instrument used to measure the cultural awareness beliefs and problem-solving strategies of pre-service mathematics teachers created by the Knowledge for Teaching Algebra ...