TopicOnFoundationsOfQuantumAlgebraicTopology 2009-04-19 06:03:25 2009-04-19 06:03:25 Topic %% Title: Quantum Algebraic Topology Foundations %%I. C. Baianu, J. F. Glazebrook and R. 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Several suggested new QAT topics are:} \begin{enumerate} \item Poisson algebras, Quantization methods and Hamiltonian algebroids \item K-S Theorem and its Quantum algebraic consequences in QAT \item Logic Lattice algebras or Many-Valued (MV) Logic algebras \item Quantum MV-Logic algebras and $\L{}-M_n$-noncommutative algebras \item Quantum Operator Algebras ( such as : involution, *-algebras, or $*$-algebras, von Neumann algebras, JB- and JL- algebras, $C^*$ - or C*- algebras, etc. \item Quantum von Neumann algebra and subfactors \item Kac-Moody and K-algebras \item Hopf algebras, Quantum Groups and Quantum group algebras \item Quantum Groupoids and weak Hopf $C^*$-algebras \item Groupoid C*-Convolution algebras and *-Convolution Algebroids \item Quantum Spacetimes and Quantum Fundamental Groupoids \item Quantum Double Algebras \item Quantum Gravity, supersymmetries, supergravity, superalgebras and graded `Lie' algebras \item Quantum Categorical algebra and Higher Dimensional, $\L{}-M_n$- Toposes \item Quantum R-categories, R-supercategories and Symmetry Breaking \item Extended Quantum Symmetries in Higher Dimensional Algebras (HDA), such as: \\ algebroids, double algebroids, categorical algebroids, double groupoids, \\ convolution algebroids, groupoid $C^*$ -convolution algebroids \item Universal algebras in R-Supercategories \item Supercategorical algebras (SA) as concrete interpretations of the Theory of Elementary Abstract Supercategories (ETAS). \item Quantum Non-Abelian Algebraic Topology (QNAAT) \item Noncommutative Geometry, Quantum Geometry, and Non-Abelian Quantum Algebraic Geometry \item Other -- Miscellaneous \textbf{[please add here your additions, changes, editing, remarks, proofs, conjectures, and so on...]} \end{enumerate} \begin{thebibliography} {9} \bibitem{AS} Alfsen, E.M. and F. 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