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## A Note About the Trace Functions on Mantaci--Reutenauer Algebra

#### Hasan Arslan [1]

##### 52 105

In this paper, we obtain the trace functions of Mantaci-Reutenauer algebra $\mathcal{MR}(W_{n})$, where $(W_{n},S_{n})$ is a Coxeter system of type $B_{n}$. We also show for every $\lambda \in \mathcal{DP}(n)$ that each characteristic class function $e_{\lambda}$ of the group $W_{n}$ is a trace function of Mantaci-Reutenauer algebra, where $\mathcal{DP}(n)$ stands for the set of all double partitions of $n$. Since the dimension of the trace function space on the Mantaci-Reutenauer algebra is $|\mathcal{DP}(n)|$, it exactly coincides with the algebra $\mathbb{Q}\textrm{Irr}W_{n}$ generated by the irreducible characters of the group $W_{n}$. Although the multiplication of basis elements $d_{A}$ and $d_{A'}$ is not commutative in Mantaci-Reutenauer algebra, the images of $d_{A}d_{A'}$ and $d_{A'}d_{A}$ under $e_{\lambda}$ are equal to each other.

Mantaci-Reutenauer algebra, Orthogonal primitive idempotent, Trace function
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Primary Language en Engineering Articles Author: Hasan ArslanInstitution: Erciyes University, Faculty of Science, Mathematics Department, Melikgazi, KayseriCountry: Turkey
 Bibtex @research article { konuralpjournalmath317697, journal = {Konuralp Journal of Mathematics (KJM)}, issn = {}, eissn = {2147-625X}, address = {Mehmet Zeki SARIKAYA}, year = {2018}, volume = {6}, pages = {140 - 143}, doi = {}, title = {A Note About the Trace Functions on Mantaci--Reutenauer Algebra}, key = {cite}, author = {Arslan, Hasan} } APA Arslan, H . (2018). A Note About the Trace Functions on Mantaci--Reutenauer Algebra. Konuralp Journal of Mathematics (KJM), 6 (1), 140-143. Retrieved from http://dergipark.gov.tr/konuralpjournalmath/issue/31478/317697 MLA Arslan, H . "A Note About the Trace Functions on Mantaci--Reutenauer Algebra". Konuralp Journal of Mathematics (KJM) 6 (2018): 140-143 Chicago Arslan, H . "A Note About the Trace Functions on Mantaci--Reutenauer Algebra". Konuralp Journal of Mathematics (KJM) 6 (2018): 140-143 RIS TY - JOUR T1 - A Note About the Trace Functions on Mantaci--Reutenauer Algebra AU - Hasan Arslan Y1 - 2018 PY - 2018 N1 - DO - T2 - Konuralp Journal of Mathematics (KJM) JF - Journal JO - JOR SP - 140 EP - 143 VL - 6 IS - 1 SN - -2147-625X M3 - UR - Y2 - 2018 ER - EndNote %0 Konuralp Journal of Mathematics (KJM) A Note About the Trace Functions on Mantaci--Reutenauer Algebra %A Hasan Arslan %T A Note About the Trace Functions on Mantaci--Reutenauer Algebra %D 2018 %J Konuralp Journal of Mathematics (KJM) %P -2147-625X %V 6 %N 1 %R %U ISNAD Arslan, Hasan . "A Note About the Trace Functions on Mantaci--Reutenauer Algebra". Konuralp Journal of Mathematics (KJM) 6 / 1 (April 2018): 140-143.