Minimal system of defining relations for some lie superalgebras

1997 ◽  
Vol 31 (1) ◽  
pp. 70-73 ◽  
Author(s):  
G. I. Prosvetov
Keyword(s):  
Minimal System ◽  
Lie Superalgebras ◽  
Defining Relations

scholarly journals DEFINING RELATIONS OF ALMOST AFFINE (HYPERBOLIC) LIE SUPERALGEBRAS

2010 ◽  
Vol 17 (sup1) ◽  
pp. 163-168 ◽  
Author(s):  
SOFIAN BOUARROUDJ ◽  
PAVEL GROZMAN ◽  
DIMITRY LEITES
Keyword(s):  
Lie Superalgebras ◽  
Defining Relations

Toward living nanomachines

2018 ◽  
Author(s):  
Christof Mast ◽  
Friederike Möller ◽  
Moritz Kreysing ◽  
Severin Schink ◽  
Benedikt Obermayer ◽  
...  
Keyword(s):  
Molecular Evolution ◽  
Thermal Gradient ◽  
Molecular Level ◽  
Minimal System ◽  
Thermal Gradients ◽  
Temperature Oscillations ◽  
Fluid Convection ◽  
Inanimate Matter ◽  
High Concentrations ◽  
Periodic Temperature

How does inanimate matter become transformed into animate matter? Living systems evolve by replication and selection at the molecular level and this chapter considers how to establish a synthetic, minimal system that can support molecular evolution and thus life. Molecular evolution cannot be explained by starting with high concentrations of activated chemicals that react toward their chemical equilibrium; persistent non-equilibria are required to maintain continuous reactivity and we especially consider thermal gradients as an early driving force for Darwinian molecular evolution. The temperature difference across water-filled compartments implements a laminar fluid convection with periodic temperature oscillations that allow for the melting and replication of DNA. Simultaneously, dissolved molecules are moved along the thermal gradient by an effect called thermophoresis. The combined result is an efficient molecule trap that exponentially favors long over short DNA and thus maintains complexity. Future experiments will reveal how thermal gradients could actively drive the Darwinian process of replication and selection.

scholarly journals Irreducible modules with highest weight vectors over modular Witt and special Lie superalgebras

2019 ◽  
Vol 17 (1) ◽  
pp. 1381-1391
Author(s):  
Keli Zheng ◽  
Yongzheng Zhang
Keyword(s):  
Lie Superalgebras ◽  
Arbitrary Field ◽  
Special Linear ◽  
Highest Weight ◽  
Irreducible Modules

Abstract Let 𝔽 be an arbitrary field of characteristic p > 2. In this paper we study irreducible modules with highest weight vectors over Witt and special Lie superalgebras of 𝔽. The same irreducible modules of general and special linear Lie superalgebras, which are the 0-th part of Witt and special Lie superalgebras in certain ℤ-grading, are also considered. Then we establish a certain connection called a P-expansion between these modules.

scholarly journals Multidimensional Multiplicative Combinatorial Properties of Dynamical Syndetic Sets

2021 ◽  
Author(s):  
Jiahao Qiu ◽  
Jianjie Zhao
Keyword(s):  
Normal Subgroup ◽  
Finite Index ◽  
Minimal System ◽  
Combinatorial Properties ◽  
Return Times ◽  
Residual Set ◽  
Closed Sets ◽  
Open Set ◽  
Geometric Progressions ◽  
Set Of Points

AbstractIn this paper, it is shown that for a minimal system (X, G), if H is a normal subgroup of G with finite index n, then X can be decomposed into n components of closed sets such that each component is minimal under H-action. Meanwhile, we prove that for a residual set of points in a minimal system with finitely many commuting homeomorphisms, the set of return times to any non-empty open set contains arbitrarily long geometric progressions in multidimension, extending a previous result by Glasscock, Koutsogiannis and Richter.

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