2011/03/15 by V. Anagnostopoulos, Anagnostopoulos, V., Yannis Sarantopoulos +2
Mathematics · #15A69 (Secondary) #16T05 (Primary) #FOS: Mathematics #Mathematics and Applications #Quantum Algebra (math.QA) #math.QA #msc:15A69 #msc:16T05
paper · pdf · doi:10.48550/arxiv.1103.2933
arxiv created 2011/03/15 · openalex publication_date 2011/03/15 · arxiv updated 2011/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We equip the tensor algebra of a vector space U over the real or complex field with an alternative product. The new product has the property that if we specialize it to the symmetric tensor algebra becomes the circle product introduced by Brouder while specialization to the antisymmetric algebra becomes the circle product introduced by Rota and Stein. We prove some interesting properties of this product analogous to the properties proved by the previous authors. We use Hopf algebraic methods to simplify our results. Finally we prove that the classical algebraic structure of the tensor algebra and the new one are homomorphically isomorphic.\bigskip