In noncommutative algebraic geometry, quadric hypersurfaces are major objects of study. this paper, we focus on studying conics ProjncA embedded into Calabi-Yau quantum projective planes. particular, give complete classifications homogeneous coordinate algebras A up to isomorphism graded algebras, and noncommutive schemes.

A new class of infinite dimensional simple Lie algebras over a field with characteristic 0 are constructed. These are examples of non-graded Lie algebras. The isomorphism classes of these Lie algebras are determined. The structure space of these algebras is given explicitly.

In this paper, a semigroup algebra consisting of polynomial expressions with coefficients in field F and exponents an additive submonoid M Q≥0 is called Puiseux denoted by F[M]. Here we study the atomic structure algebras. To begin with, answer isomorphism problem for class algebras, that is, show if two algebras F[M1] F[M2] are isomorphic, then monoids M1 M2 must be isomorphic. Then construct ...

Let M be a closed, oriented, n-manifold, and LM its free loop space. In [C-S1] a commutative algebra structure in homology, H∗(LM), and a Lie algebra structure in equivariant homology H 1 ∗ (LM), were defined. In this paper we prove that these structures are homotopy invariant for simply connected manifolds in the following sense. Let f : M1 → M2 be a homotopy equivalence of simply connected cl...

We introduce an algorithm to decide isomorphism between tensors. The uses the Lie algebra of derivations a tensor compress space in which search takes place so-called densor space. To make method practicable we give polynomial-time solve generalization module for common class modules. As consequence, show that testing is polynomial time tensors whose derivation algebras are classical and spaces...

We study the isomorphism problem of two “natural” algebraic structures – F-algebras and cubic forms. We prove that the F-algebra isomorphism problem reduces in polynomial time to the cubic forms equivalence problem. This answers a question asked in [AS05]. For finite fields of the form 3 6 |(#F − 1), this result implies that the two problems are infact equivalent. This result also has the follo...