2025/09/12 by Smoktunowicz, Agata
#16S80 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2509.10121
We say that a formal deformation from an algebra N to algebra A is strongly flat if for every real number e there is a real number 00 gives an algebra isomorphic to A. It is shown that all semisimple algebras which can be obtained as a specialisation of such a deformation are isomorphic. We also show that every strongly flat deformation \mathcal N=N\t\ from a finite-dimensional \mathbb C-algebra N to a semisimple \mathbb C-algebra A specialised at t=s for all sufficiently small real numbers s>0 gives an algebra isomorphic to A. A remark by Joachim Jelisiejew is also included which allows us to obtain this result as an application of Gabriel's theorem [6]. We also give a characterisation of semisimple algebras A to which a given algebra N cannot be deformed to. This gives a partial answer to a question of Michael Wemyss on Acons [26]. We also give a partial answer to question 6.5 from [1].