The Real Forms of the Fractional Supergroup SL(2,C)

Ucan, Yasemen; Köşker, Reşat

doi:10.3390/math9090933

Cited by 2 publications

(2 citation statements)

References 24 publications

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“…The USA should take measures to reverse the temperature rise and determine environmental policies in the fact that air temperature rise will be a major problem for the world in the future. We hope that this model we propose can be developed for fractional supergroup SU(2) [18], the real form of fractional supergroup SL(2, C).…”

Section: Discussionmentioning

confidence: 99%

Air temperature measurement based on lie group SO(3)

Ucan

Bildirici

2022

Therm sci

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This study aims to analyze the behaviors of air temperature during the period from 1895(5) to 2021(12) using Lie algebras method. We proposed an alternative method to model air temperature, in which the non-linear structure of temperature is evolved by a stochastic differential equation captured on a curved state space. After expressing stochastic differential equations based on Lie algebras and Lie groups, we tested the non-linear and random behavior of air temperature. This method allow a rich geometric structure. Moreover diffusion processes can easily be built without needing the machinery of stochastic calculus on manifolds.

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Section: Discussionmentioning

confidence: 99%

Air temperature measurement based on lie group SO(3)

Ucan

Bildirici

2022

Therm sci

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“…As a suggestion for future papers, the usage of this method to solve open problems in applied mathematics, economics, and financial mathematics will provide important contributions. On the other hand, because the use of supersymmetries in engineering and physics is common and very important, using the fractional super group, SU(2), which is one of the real forms of the fractional super group, SL(2,C), obtained in Ucan and Kosker [22], to solve this model is suggested in future papers.…”

Section: Discussionmentioning

confidence: 99%

Interest Rate Based on The Lie Group SO(3) in the Evidence of Chaos

2022

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This paper aims to test the structure of interest rates during the period from 1 September 1981 to 28 December 2020 by using Lie algebras and groups. The selected period experienced substantial events impacting interest rates, such as the economic crisis, the military intervention of the USA in Iraq, and the COVID-19 pandemic, in which economies were in lockdown. These conditions caused the interest rate to have a nonlinear structure, chaotic behavior, and outliers. Under these conditions, an alternative method is proposed to test the random and nonlinear structure of interest rates to be evolved by a stochastic differential equation captured on a curved state space based on Lie algebras and group. Then, parameter estimates of this equation were obtained by OLS, NLS, and GMM estimators (hereafter, LieNLS, LieOLS, and LieGMM, respectively). Therefore, the interest rates that possess nonlinear structures and/or chaotic behaviors or outliers were tested with LieNLS, LieOLS, and LieGMM. We compared our LieNLS, LieOLS, and LieGMM results with the traditional OLS, NLS, and GMM methods, and the results favor the improvement achieved by the proposed LieNLS, LieOLS, and LieGMM in terms of the RMSE and MAE in the out-of-sample forecasts. Lastly, the Lie algebras with NLS estimators exhibited the lowest RMSE and MAE followed by the Lie algebras with GMM, and the Lie algebras with OLS, respectively.

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The Real Forms of the Fractional Supergroup SL(2,C)

Cited by 2 publications

References 24 publications

Air temperature measurement based on lie group SO(3)

Air temperature measurement based on lie group SO(3)

Interest Rate Based on The Lie Group SO(3) in the Evidence of Chaos

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