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We investigate structure of $^{13}_\Lambda{\rm C}$ and discuss the differenceand similarity between the structures of $^{12}{\rm C}$ and $^{13}_\Lambda{\rmC}$ by answering the questions if the linear-chain and gaslike cluster states,which are proposed to appear in $^{12}{\rm C}$, survives, or new structurestates appear or not. We introduce a microscopic cluster model called,Hyper-Tohsaki-Horiuchi-Schuck-R\"opke (H-THSR) wave function, which is anextended version of the THSR wave function so as to describe $\Lambda$hypernuclei. We obtained two bound states and two resonance (quasi-bound)states for $J^\pi=0^+$ in $^{13}_\Lambda{\rm C}$, corresponding to the four$0^+$ states in $^{12}{\rm C}$. However, the inversion of level orderingbetween the spectra of $^{12}{\rm C}$ and $^{13}_\Lambda{\rm C}$, i.e. that the$0_3^+$ and $0_4^+$ states in $^{13}_\Lambda{\rm C}$ correspond to the $0_4^+$and $0_3^+$ states in $^{12}{\rm C}$, respectively, is shown to occur. Theadditional $\Lambda$ particle reduces sizes of the $0_2^+$ and $0_3^+$ statesin $^{13}_\Lambda{\rm C}$ very much, but the shrinkage of the $0_4^+$ state isonly a half of the other states. In conclusion, the Hoyle state becomes quite acompact object with ${^{9}_\Lambda{\rm Be}}+\alpha$ configuration in$^{13}_\Lambda{\rm C}$ and is no more gaslike state composed of the $3\alpha$clusters. Instead, the $0_4^+$ state in $^{13}_\Lambda{\rm C}$, coming from the$^{12}{\rm C}(0_3^+)$ state, appears as a gaslike state composed of$\alpha+\alpha+^{5}_\Lambda{\rm He}$ configuration, i.e. the Hoyle analogstate. A linear-chain state in a $\Lambda$ hypernucleus is for the first timepredicted to exist as the $0_3^+$ state in $^{13}_\Lambda{\rm C}$ with moreshrunk arrangement of the $3\alpha$ clusters along $z$-axis than the $3\alpha$linear-chain configuration realized in the $^{12}{\rm C}(0_4^+)$ state.

Multi-cluster dynamics in $^{13}_\Lambda{\rm C}$ and analogy to clustering in $^{12}{\rm C}$