Uncountably many non-commensurable pro-p groups of homological type FPk but not FPk+1

2019 ◽  
Vol 29 (07) ◽  
pp. 1219-1234 ◽  
Author(s):  
Dessislava Kochloukova
Keyword(s):  
Type Formula ◽  
Finitely Presented ◽  
Text Element ◽  
Homological Type

We show that there are uncountably many non-commensurable metabelian pro-[Formula: see text] groups of homological type [Formula: see text] but not of type [Formula: see text], generated by [Formula: see text] element, where [Formula: see text] and [Formula: see text]. In particular there are uncountably many non-commensurable finitely presented metabelian pro-[Formula: see text] groups that are not of type [Formula: see text]. We show furthermore that there are uncountably many non-isomorphic one related 2-generated pro-[Formula: see text] groups.

SOME EXACT SEQUENCES FOR THE HOMOTOPY (BI-)MODULE OF A MONOID

2002 ◽  
Vol 12 (01n02) ◽  
pp. 247-284 ◽  
Author(s):  
YUJI KOBAYASHI ◽  
FRIEDRICH OTTO
Keyword(s):  
Finiteness Conditions ◽  
Type Formula ◽  
Homotopy Module ◽  
The Relationship ◽  
Finite Derivation Type ◽  
Finitely Presented ◽  
Exact Sequences ◽  
Homological Type

For finitely presented monoids the homological finiteness conditions left-[Formula: see text], left-[Formula: see text], right-[Formula: see text] and right-[Formula: see text], the homotopical finiteness conditions of having finite derivation type [Formula: see text] and of being of finite homological type [Formula: see text] are developed and the relationship between these notions is investigated in detail. In particular, a result of Pride [40] and Guba and Sapir [27] on the exactness of a sequence of bimodules for the homotopy module is proved in a completely different, purely combinatorial manner. This proof is then translated into a proof of the corresponding result for the left homotopy module, thus giving new insights into the relationship between the finiteness conditions considered.

Intermediate growth in finitely presented algebras

2017 ◽  
Vol 27 (04) ◽  
pp. 391-401 ◽  
Author(s):  
Dilber Koçak
Keyword(s):  
Lie Algebras ◽  
Associative Algebras ◽  
Intermediate Growth ◽  
Type Formula ◽  
Growth Types ◽  
Finitely Presented

For any integer [Formula: see text], we construct examples of finitely presented associative algebras over a field of characteristic [Formula: see text] with intermediate growth of type [Formula: see text]. We produce these examples by computing the growth types of some finitely presented metabelian Lie algebras.

scholarly journals Finite presentability of some metabelian Hopf algebras

2005 ◽  
Vol 72 (1) ◽  
pp. 109-127 ◽  
Author(s):  
Dessislava H. Kochloukova
Keyword(s):  
Abelian Group ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Hopf Algebras ◽  
Abelian Ideal ◽  
Finite Presentability ◽  
Finitely Presented ◽  
Homological Type

We classify the Hopf algebras U (L)#kQ of homological type FP2 where L is a Lie algebra and Q an Abelian group such that L has an Abelian ideal A invariant under the Q-action via conjugation and U (L/A)#kQ is commutative. This generalises the classification of finitely presented metabelian Lie algebras given by J. Groves and R. Bryant.

A construction of a finitely presented semigroup containing an infinite square-free ideal with zero multiplication

2018 ◽  
Vol 28 (08) ◽  
pp. 1565-1573 ◽  
Author(s):  
Ilya Ivanov-Pogodaev ◽  
Sergey Malev ◽  
Olga Sapir
Keyword(s):  
Type Formula ◽  
Zero Multiplication ◽  
Finitely Presented

This work provides an example of a finitely presented semigroup [Formula: see text] with zero containing an infinite ideal of the form [Formula: see text], where [Formula: see text] is a generator of [Formula: see text], such that every word in generators representing an element of [Formula: see text] is square free (i.e. any word of the type [Formula: see text], for non-empty [Formula: see text], equals zero in [Formula: see text]).

Homological Finite Derivation Type

2003 ◽  
Vol 13 (03) ◽  
pp. 341-359 ◽  
Author(s):  
Juan M. Alonso ◽  
Susan M. Hermiller
Keyword(s):  
Free Monoid ◽  
Higher Dimensions ◽  
Finiteness Condition ◽  
Finitely Generated ◽  
Monoid Ring ◽  
Finite Derivation Type ◽  
Finitely Presented ◽  
Homological Type

In 1987, Squier defined the notion of finite derivation type for a finitely presented monoid. To do this, he associated a 2-complex to the presentation. The monoid then has finite derivation type if, modulo the action of the free monoid ring, the 1-dimensional homotopy of this complex is finitely generated. Cremanns and Otto showed that finite derivation type implies the homological finiteness condition left FP3, and when the monoid is a group, these two properties are equivalent. In this paper we define a new version of finite derivation type, based on homological information, together with an extension of this finite derivation type to higher dimensions, and show connections to homological type FPnfor both monoids and groups.

scholarly journals Verlinde formulae on complex surfaces: K-theoretic invariants

2021 ◽  
Vol 9 ◽  
Author(s):  
L. Göttsche ◽  
M. Kool ◽  
R. A. Williams
Keyword(s):  
Moduli Space ◽  
K3 Surfaces ◽  
Complex Surfaces ◽  
Type Formula ◽  
Verlinde Formula ◽  
Donaldson Invariants

Abstract We conjecture a Verlinde type formula for the moduli space of Higgs sheaves on a surface with a holomorphic 2-form. The conjecture specializes to a Verlinde formula for the moduli space of sheaves. Our formula interpolates between K-theoretic Donaldson invariants studied by Göttsche and Nakajima-Yoshioka and K-theoretic Vafa-Witten invariants introduced by Thomas and also studied by Göttsche and Kool. We verify our conjectures in many examples (for example, on K3 surfaces).

scholarly journals A Class of Integral Operators that Fix Exponential Functions

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Carlo Bardaro ◽  
Ilaria Mantellini ◽  
Gumrah Uysal ◽  
Basar Yilmaz
Keyword(s):  
General Class ◽  
Pointwise Convergence ◽  
Type Theorem ◽  
Integral Operators ◽  
Exponential Functions ◽  
Convergence Theorems ◽  
Korovkin Type Theorem ◽  
Type Formula

AbstractIn this paper we introduce a general class of integral operators that fix exponential functions, containing several recent modified operators of Gauss–Weierstrass, or Picard or moment type operators. Pointwise convergence theorems are studied, using a Korovkin-type theorem and a Voronovskaja-type formula is obtained.

scholarly journals Uniqueness of Curvature Measures in Pseudo-Riemannian Geometry

2021 ◽  
Author(s):  
Andreas Bernig ◽  
Dmitry Faifman ◽  
Gil Solanes
Keyword(s):  
Riemannian Manifolds ◽  
Riemannian Geometry ◽  
Riemannian Space ◽  
Space Forms ◽  
Type Formula ◽  
Isometric Embeddings ◽  
Curvature Measures ◽  
Riemannian Space Forms

AbstractThe recently introduced Lipschitz–Killing curvature measures on pseudo-Riemannian manifolds satisfy a Weyl principle, i.e. are invariant under isometric embeddings. We show that they are uniquely characterized by this property. We apply this characterization to prove a Künneth-type formula for Lipschitz–Killing curvature measures, and to classify the invariant generalized valuations and curvature measures on all isotropic pseudo-Riemannian space forms.

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