C*-algebras associated to topological Ore semigroups

Let $G$ be a locally compact group and $P \subset G$ be a closed Ore semigroup containing the identity element. Let V: P \to B(\clh) be a representation such that for every $a \in P$, $V_{a}$ is an isometry and the final projections of $\{V_{a}: a \in P\}$ commute. In this article, we study the $C^{*}$-algebra $\mathcal{W}_{V}(P,G)$, generated by $\{\int f(a)V_{a} da: f \in L^{1}(P)\}$. We show that there exists a universal $C^{*}$-algebra, which admits a groupoid description, of which $\mathcal{W}_{V}(P,G)$ is a quotient. If $P=G$, then this universal algebra is just $C^{*}(G)$

Cuntz-Li relations, Inverse semigroups and Groupoids

In this paper we show that the universal C*-algebra satisfying the Cuntz-Li relations is generated by an inverse semigroup of partial isometries. We apply Exel's theory of tight representations to this inverse semigroup. We identify the universal C*-algebra as the C*-algebra of the tight groupoid associated to the inverse semigroup.Comment: Section 8 has undergone substantial revisions. More proofs adde

Inverse semigroups and the Cuntz-Li algebras

In this paper, we apply the theory of inverse semigroups to the $C^{*}$-algebra $U[\mathbb{Z}]$ considered in \cite{Cuntz}. We show that the $C^{*}$-algebra $U[\mathbb{Z}]$ is generated by an inverse semigroup of partial isometries. We explicity identify the groupoid $\mathcal{G}_{tight}$ associated to the inverse semigroup and show that $\mathcal{G}_{tight}$ is exactly the same groupoid obtained in \cite{Cuntz-Li}.Comment: A section added on Nica covariance and boundary relations. Few typos correcte

Farmers\u27 Perception on the Performance of Different Rice Varieties in Kapilvastu District, Nepal

Rice is the major staple food crop in Nepal. To date, several rice varieties have been developed and released in Nepal. However, rice production is far below in comparison with its production potential. A household survey was conducted in Bangaganga municipality of Kapilvastu district in 2018 to assess farmers\u27 perception on performance of four different rice varieties (Radha-4, Ramdhan, Gorakhnath, and Sawa). The data were collected from a total of 120 rice farmers (randomly selected) using the interview schedule and analyzed using descriptive statistics, Likert scale, and indexing technique. Statistical analysis showed that the Ramdhan variety had the highest yield (4.95 t/ha), whereas Radha-4 had the lowest yield (3.15 t/ha). The most disease and drought-tolerant variety, as perceived by the farmers, was Radha-4. Smut and Khaira were perceived as the primary diseases whereas Brown planthopper and Rice Gundhi bug were the most important insects of all studied rice varieties. The study recommended that the plant breeders should focus on developing site-specific rice varieties to meet the multiple concerns of the farmers, such as higher yield and stress-tolerant. The farmers should be made aware of varietal selection and crop pest management techniques via training programs, which further helps to reduce the yield gap between farmers\u27 field and research field