Minimal Varieties of Algebras of Exponential Growth
نویسندگان
چکیده
The exponent of a variety of algebras over a field of characteristic zero has been recently proved to be an integer. Through this scale we can now classify all minimal varieties of a given exponent and of finite basic rank. As a consequence we describe the corresponding T-ideals of the free algebra, and we compute the asymptotics of the related codimension sequences. We then verify in this setting some known conjectures.
منابع مشابه
Classification of algebras with minimal quadratic growth of identities
The main goal of this paper is to prove that the five algebras which were used in [3] to classify (up to PI-equivalence) the algebras whose sequence of codimensions is bounded by a linear function generate the only five minimal varieties of quadratic growth.
متن کاملOn growth of Lie algebras, generalized partitions, and analytic functions
In this paper we discuss some recent results on two diierent types of growth of Lie algebras, that lead to some combinatorial problems. First, we study the growth of nitely generated Lie algebras (sections 1{4). This problem leads to a study of generalized partitions. Recently the author has suggested a series of q-dimensions of algebras Dim q , q 2 N which includes, as rst terms, dimensions of...
متن کاملRectangular Algebras as Tree Recognizers
We consider finite rectangular algebras of finite type as tree recognizers. The type is represented by a ranked alphabet Σ. We determine the varieties of finite rectangular Σ-algebras and show that they form a Boolean lattice in which the atoms are minimal varieties of finite Σ-algebras consisting of projection algebras. We also describe the corresponding varieties of Σ-tree languages and compa...
متن کاملRisk measurement and Implied volatility under Minimal Entropy Martingale Measure for Levy process
This paper focuses on two main issues that are based on two important concepts: exponential Levy process and minimal entropy martingale measure. First, we intend to obtain risk measurement such as value-at-risk (VaR) and conditional value-at-risk (CvaR) using Monte-Carlo methodunder minimal entropy martingale measure (MEMM) for exponential Levy process. This Martingale measure is used for the...
متن کاملMinimal Varieties and Quasivarieties of Semilattices with One Automorphism
We describe all minimal quasivarieties and all minimal varieties of semilattices with one automorphism (considered as algebras with one binary and two unary operations).
متن کامل