An algebraic model for rational torus-equivariant spectra

AbstractThe category of rational SO(2)–equivariant spectra admits an algebraic model. That is, there is an abelian category ${\mathcal A}$(SO(2)) whose derived category is equivalent to the homotopy category of rational SO(2)–equivariant spectra. An important question is: does this algebraic model capture the smash product of spectra?The category ${\mathcal A}$(SO(2)) is known as Greenlees' standard model, it is an abelian category that has no projective objects and is constructed from modules over a non–Noetherian ring. As a consequence, the standard techniques for constructing a monoidal model structure cannot be applied. In this paper a monoidal model structure on ${\mathcal A}$(SO(2)) is constructed and the derived tensor product on the homotopy category is shown to be compatible with the smash product of spectra. The method used is related to techniques developed by the author in earlier joint work with Roitzheim. That work constructed a monoidal model structure on Franke's exotic model for the K(p)–local stable homotopy category.A monoidal Quillen equivalence to a simpler monoidal model category R•-mod that has explicit generating sets is also given. Having monoidal model structures on ${\mathcal A}$(SO(2)) and R•-mod removes a serious obstruction to constructing a series of monoidal Quillen equivalences between the algebraic model and rational SO(2)–equivariant spectra.

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TESTING AN ALGEBRAIC MODEL OF SELF-REFLEXION

Perceptual and Motor Skills ◽

10.2466/pms.100.4.1036-1048 ◽

2005 ◽

Vol 100 (4) ◽

pp. 1036 ◽

Cited By ~ 3

Author(s):

JAMES W. GRICE

Keyword(s):

Algebraic Model

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Vibrational spectra of NCCN, CNCN and CNNC : a study using the U(4) algebraic model

Vibrational Spectroscopy ◽

10.1016/j.vibspec.2020.103032 ◽

2020 ◽

Vol 107 ◽

pp. 103032 ◽

Cited By ~ 2

Author(s):

Nirmal Kumar Sarkar

Keyword(s):

Vibrational Spectra ◽

Algebraic Model

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Geometrical Structure of Constraint Manifold in Power System Differential-Algebraic Model

2006 International Conference on Power System Technology ◽

10.1109/icpst.2006.321597 ◽

2006 ◽

Cited By ~ 1

Author(s):

H. Wu ◽

R. Guo ◽

Z. Han ◽

D. Gan

Keyword(s):

Power System ◽

Geometrical Structure ◽

Algebraic Model ◽

Constraint Manifold

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RATIONAL LOCAL SYSTEMS AND CONNECTED FINITE LOOP SPACES

Glasgow Mathematical Journal ◽

10.1017/s0017089520000658 ◽

2021 ◽

pp. 1-29

Author(s):

DREW HEARD

Keyword(s):

Lie Group ◽

Loop Space ◽

Algebraic Model ◽

Compact Lie Group ◽

Loop Spaces ◽

Local Systems ◽

Special Case ◽

Finite Loop ◽

Finite Loop Space

Abstract Greenlees has conjectured that the rational stable equivariant homotopy category of a compact Lie group always has an algebraic model. Based on this idea, we show that the category of rational local systems on a connected finite loop space always has a simple algebraic model. When the loop space arises from a connected compact Lie group, this recovers a special case of a result of Pol and Williamson about rational cofree G-spectra. More generally, we show that if K is a closed subgroup of a compact Lie group G such that the Weyl group W G K is connected, then a certain category of rational G-spectra “at K” has an algebraic model. For example, when K is the trivial group, this is just the category of rational cofree G-spectra, and this recovers the aforementioned result. Throughout, we pay careful attention to the role of torsion and complete categories.

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Simple Algebraic Expressions for the Prediction and Control of High-Temperature Annealed Structures by Linear Perturbation Analysis

Mathematical and Computational Applications ◽

10.3390/mca26020043 ◽

2021 ◽

Vol 26 (2) ◽

pp. 43

Author(s):

Constantino Grau Grau Turuelo ◽

Cornelia Breitkopf

Keyword(s):

High Temperature ◽

Surface Diffusion ◽

Perturbation Analysis ◽

Algebraic Model ◽

Structure Design ◽

Linear Perturbation ◽

Prediction And Control ◽

Void Shape ◽

Void Structure ◽

And Control

The prediction and control of the transformation of void structures with high-temperature processing is a critical area in many engineering applications. In this work, focused on the void shape evolution of silicon, a novel algebraic model for the calculation of final equilibrium structures from initial void cylindrical trenches, driven by surface diffusion, is introduced. This algebraic model provides a simple and fast way to calculate expressions to predict the final geometrical characteristics, based on linear perturbation analysis. The obtained results are similar to most compared literature data, especially, to those in which a final transformation is reached. Additionally, the model can be applied in any materials affected by the surface diffusion. With such a model, the calculation of void structure design points is greatly simplified not only in the semiconductors field but in other engineering fields where surface diffusion phenomenon is studied.

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