Results 61 to 70 of about 17,683 (170)

Contractions of Lie algebras and algebraic groups

Archivum Mathematicum, 2007
Degenerations, contractions and deformations of various algebraic structures play an important role in mathematics and physics. There are many different definitions and special cases of these notions. We try to give a general definition which unifies these notions and shows the connections among them.
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Geometric Algebra Quantum Gate Decomposition

Axioms
Quantum gates are traditionally described using matrix and tensor-product formalisms, representations that provide limited geometric intuition. In this work, we develop a formulation of the Pauli and Clifford groups within the complex Geometric Algebra ...
Youssef Amraoui, Zeno Toffano
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Algebraic automorphism groups [PDF]

Illinois Journal of Mathematics, 1975
For an algebraic group G, let W(G) denote the group of all algebraic group automorphisms of G. In this chapter, we examine the possibility of endowing W(G) with the structure of an algebraic group in such a way that G becomes a strict W(G)-variety. The example of a toroid of dimension greater than 1 shows that this is not always possible. However, good
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Efficient Computations

Современные информационные технологии и IT-образование
This article considers a computational method that is more efficient than methods based on the divide-and-conquer principle. Goethe once said that divide and conquer is a good principle, but the principle of unite and guide is better.
Rustem Aidagulov, Valery Vasenin
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Group algebras and coding theory: a short survey

Revista Integración, 2019
We study codes constructed from ideals in group algebras and we are particularly interested in their dimensions and weights. First we introduced a special kind of idempotents and study the ideals they generate.
César Polcino Milies
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Exponentiality of Algebraic Groups

Journal of Algebra, 1996
A connected real Lie group \(G\) is called exponential if the exponential map from the Lie algebra of \(G\) to \(G\) is surjective. The question of which connected real Lie groups are exponential has long been a matter of interest and was investigated by several authors.
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Unit group of algebra of circulant matrices [PDF]

International Journal of Group Theory, 2013
Let Crn(Fp) denote the algebra of nXn circulant matrices over Fp, finite field of order p of prime characteristic p. The order of the unit groups U(Cr3(Fp)), U(Cr4(Fp)) and U(Cr5(Fp)) of algebras of circulant matrices over Fp are characterized.
Rajendra Sharma, Pooja Yadav
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The unit group of algebra of circulant matrices [PDF]

International Journal of Group Theory, 2014
Let $Cr_{n}(F)$ denote the algebra of $n times n$ circulant matrices over the field $F$. In this paper, we study the unit group of $Cr_{n}(F_{p^m})$, where $F_{p^m}$ denotes the Galois field of order $p^{m}$, $p$ prime.
Neha Makhijani , 2R. K. Sharma, J. B. Srivastava   +2 more
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Units in $F_{2^k}D_{2n}$ [PDF]

International Journal of Group Theory, 2014
Let $F_q D_{2n}$ be the group algebra of $D_{2n}$, the dihedral group of order $2n$ over $F_q=GF(q)$. In this paper, we establish the structure of $U(F_{2^k}D_{2n})$, the unit group of $F_{2^k}D_{2n}$ and that of its normalized unitary subgroup $V_*(F_{2^
Neha Makhijani , R. Sharma, 2J. B. Srivastava   +2 more
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The derivation algebra and automorphism group of the electrical Lie algebra of type D5

上海师范大学学报. 自然科学版
In this paper, we mainly investigate the derivation algebra and automorphism group of type D5 electrical Lie algebra. We prove that the outer derivations are four-dimensional, and the automorphism group Aut $\mathcal{L} \cong \mathbb{C}^* \ltimes\left ...
LI Zhiling, SHEN Ran
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